[{"volume":36,"quality_controlled":"1","citation":{"short":"G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Mathematical Models and Methods in Applied Sciences 36 (2026) 1185–1233.","ista":"Auricchio G, Brigati G, Giudici P, Toscani G. 2026. From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. Mathematical Models and Methods in Applied Sciences. 36(6), 1185–1233.","ieee":"G. Auricchio, G. Brigati, P. Giudici, and G. Toscani, “From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 36, no. 6. World Scientific Publishing, pp. 1185–1233, 2026.","mla":"Auricchio, Gennaro, et al. “From Kinetic Theory to AI: A Rediscovery of High-Dimensional Divergences and Their Properties.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 36, no. 6, World Scientific Publishing, 2026, pp. 1185–233, doi:<a href=\"https://doi.org/10.1142/S0218202526410010\">10.1142/S0218202526410010</a>.","apa":"Auricchio, G., Brigati, G., Giudici, P., &#38; Toscani, G. (2026). From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202526410010\">https://doi.org/10.1142/S0218202526410010</a>","ama":"Auricchio G, Brigati G, Giudici P, Toscani G. From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties. <i>Mathematical Models and Methods in Applied Sciences</i>. 2026;36(6):1185-1233. doi:<a href=\"https://doi.org/10.1142/S0218202526410010\">10.1142/S0218202526410010</a>","chicago":"Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. “From Kinetic Theory to AI: A Rediscovery of High-Dimensional Divergences and Their Properties.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026. <a href=\"https://doi.org/10.1142/S0218202526410010\">https://doi.org/10.1142/S0218202526410010</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1142/S0218202526410010","scopus_import":"1","article_processing_charge":"No","author":[{"first_name":"Gennaro","last_name":"Auricchio","full_name":"Auricchio, Gennaro"},{"first_name":"Giovanni","last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni"},{"full_name":"Giudici, Paolo","first_name":"Paolo","last_name":"Giudici"},{"full_name":"Toscani, Giuseppe","first_name":"Giuseppe","last_name":"Toscani"}],"day":"01","language":[{"iso":"eng"}],"date_created":"2026-03-29T22:07:08Z","OA_place":"repository","researchdata_availability":"no","article_type":"original","acknowledgement":"This work has been written within the activities of GNCS and GNFM groups of INdAM (Italian\r\nNational Institute of High Mathematics). G.B. has been funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. P.G. has been funded by the European Union - NextGenerationEU, in the framework of the GRINSGrowing Resilient, INclusive and Sustainable (GRINS PE00000018).","department":[{"_id":"JaMa"}],"type":"journal_article","issue":"6","date_updated":"2026-07-27T12:11:38Z","publication":"Mathematical Models and Methods in Applied Sciences","date_published":"2026-06-01T00:00:00Z","month":"06","page":"1185-1233","status":"public","mathsc":["35B40","35L60","35K55","35Q70","35Q91","35Q92"],"publisher":"World Scientific Publishing","project":[{"name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","grant_number":"101034413"}],"external_id":{"arxiv":["2507.11387"]},"supplementarymaterial":"no","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2507.11387","open_access":"1"}],"OA_type":"green","abstract":[{"lang":"eng","text":"Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback–Leibler (KL) divergence, originally introduced in kinetic theory as a measure of relative entropy between probability distributions. Just as in machine learning, the ability to quantify the proximity of probability distributions plays a central role in kinetic theory. In this paper, we present a comparative review of divergence measures rooted in kinetic theory, highlighting their theoretical foundations and exploring their potential applications in machine learning and artificial intelligence."}],"year":"2026","das_tickbox":"0","oa_version":"Preprint","title":"From kinetic theory to AI: A rediscovery of high-dimensional divergences and their properties","publication_status":"published","_id":"21504","ec_funded":1,"oa":1,"intvolume":"        36"},{"publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"external_id":{"arxiv":["2502.09550"]},"publisher":"World Scientific Publishing","mathsc":["65N30","76D07","76M10"],"oa":1,"title":"A Nitsche method for incompressible fluids with general dynamic boundary conditions","publication_status":"epub_ahead","_id":"22718","oa_version":"Preprint","abstract":[{"text":"Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour at the boundary. We examine a broad class of slip boundary conditions that generalises the commonly used Navier slip, perfect slip, stick-slip and Tresca friction boundary conditions. In particular, set-valued, nonmonotone, noncoercive and dynamic relations may occur. For a unifying framework of such relations, we present a fully discrete numerical scheme for the time-dependent Navier–Stokes equations subject to impermeability and general slip-type boundary conditions on polyhedral domains. Based on compactness arguments, we prove convergence of subsequences, finally ensuring the existence of a weak solution. The numerical scheme uses a general inf-sup stable pair of finite element spaces for the velocity and pressure, a regularisation approach for the implicit slip boundary condition and, most importantly, a general Nitsche method to impose the impermeability and a backward Euler time stepping. One of the key tools in the convergence proof is an inhomogeneous Korn inequality that includes a normal trace term.","lang":"eng"}],"year":"2026","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2502.09550"}],"OA_type":"green","arxiv":1,"article_processing_charge":"No","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1142/S0218202526500508","quality_controlled":"1","citation":{"ieee":"P. A. Gazca-Orozco, F. Gmeineder, E. Maringová, and T. Tscherpel, “A Nitsche method for incompressible fluids with general dynamic boundary conditions,” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026.","short":"P.A. Gazca-Orozco, F. Gmeineder, E. Maringová, T. Tscherpel, Mathematical Models and Methods in Applied Sciences (2026).","ista":"Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. 2026. A Nitsche method for incompressible fluids with general dynamic boundary conditions. Mathematical Models and Methods in Applied Sciences.","chicago":"Gazca-Orozco, Pablo Alexei, Franz Gmeineder, Erika Maringová, and Tabea Tscherpel. “A Nitsche Method for Incompressible Fluids with General Dynamic Boundary Conditions.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2026. <a href=\"https://doi.org/10.1142/S0218202526500508\">https://doi.org/10.1142/S0218202526500508</a>.","mla":"Gazca-Orozco, Pablo Alexei, et al. “A Nitsche Method for Incompressible Fluids with General Dynamic Boundary Conditions.” <i>Mathematical Models and Methods in Applied Sciences</i>, World Scientific Publishing, 2026, doi:<a href=\"https://doi.org/10.1142/S0218202526500508\">10.1142/S0218202526500508</a>.","apa":"Gazca-Orozco, P. A., Gmeineder, F., Maringová, E., &#38; Tscherpel, T. (2026). A Nitsche method for incompressible fluids with general dynamic boundary conditions. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202526500508\">https://doi.org/10.1142/S0218202526500508</a>","ama":"Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. A Nitsche method for incompressible fluids with general dynamic boundary conditions. <i>Mathematical Models and Methods in Applied Sciences</i>. 2026. doi:<a href=\"https://doi.org/10.1142/S0218202526500508\">10.1142/S0218202526500508</a>"},"status":"public","publication":"Mathematical Models and Methods in Applied Sciences","month":"08","date_published":"2026-08-04T00:00:00Z","date_updated":"2026-08-18T07:51:59Z","department":[{"_id":"JuFi"}],"type":"journal_article","article_type":"original","OA_place":"repository","date_created":"2026-08-16T22:01:44Z","language":[{"iso":"eng"}],"day":"04","author":[{"full_name":"Gazca-Orozco, Pablo Alexei","first_name":"Pablo Alexei","last_name":"Gazca-Orozco"},{"first_name":"Franz","last_name":"Gmeineder","full_name":"Gmeineder, Franz"},{"id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","first_name":"Erika","full_name":"Maringová, Erika"},{"full_name":"Tscherpel, Tabea","first_name":"Tabea","last_name":"Tscherpel"}]},{"issue":"5","type":"journal_article","department":[{"_id":"JaMa"}],"date_updated":"2025-09-30T11:36:56Z","date_published":"2025-05-01T00:00:00Z","month":"05","publication":"Mathematical Models and Methods in Applied Sciences","status":"public","page":"1267-1296","author":[{"first_name":"Gennaro","last_name":"Auricchio","full_name":"Auricchio, Gennaro"},{"first_name":"Giovanni","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","last_name":"Brigati","full_name":"Brigati, Giovanni"},{"full_name":"Giudici, Paolo","first_name":"Paolo","last_name":"Giudici"},{"full_name":"Toscani, Giuseppe","first_name":"Giuseppe","last_name":"Toscani"}],"language":[{"iso":"eng"}],"day":"01","date_created":"2025-04-15T13:34:00Z","OA_place":"repository","article_type":"original","scopus_import":"1","article_processing_charge":"No","isi":1,"citation":{"ieee":"G. Auricchio, G. Brigati, P. Giudici, and G. Toscani, “Multivariate Gini-type discrepancies,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 35, no. 5. World Scientific Publishing, pp. 1267–1296, 2025.","short":"G. Auricchio, G. Brigati, P. Giudici, G. Toscani, Mathematical Models and Methods in Applied Sciences 35 (2025) 1267–1296.","ista":"Auricchio G, Brigati G, Giudici P, Toscani G. 2025. Multivariate Gini-type discrepancies. Mathematical Models and Methods in Applied Sciences. 35(5), 1267–1296.","chicago":"Auricchio, Gennaro, Giovanni Brigati, Paolo Giudici, and Giuseppe Toscani. “Multivariate Gini-Type Discrepancies.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2025. <a href=\"https://doi.org/10.1142/s0218202525500174\">https://doi.org/10.1142/s0218202525500174</a>.","ama":"Auricchio G, Brigati G, Giudici P, Toscani G. Multivariate Gini-type discrepancies. <i>Mathematical Models and Methods in Applied Sciences</i>. 2025;35(5):1267-1296. doi:<a href=\"https://doi.org/10.1142/s0218202525500174\">10.1142/s0218202525500174</a>","apa":"Auricchio, G., Brigati, G., Giudici, P., &#38; Toscani, G. (2025). Multivariate Gini-type discrepancies. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0218202525500174\">https://doi.org/10.1142/s0218202525500174</a>","mla":"Auricchio, Gennaro, et al. “Multivariate Gini-Type Discrepancies.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 35, no. 5, World Scientific Publishing, 2025, pp. 1267–96, doi:<a href=\"https://doi.org/10.1142/s0218202525500174\">10.1142/s0218202525500174</a>."},"quality_controlled":"1","volume":35,"doi":"10.1142/s0218202525500174","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa_version":"Preprint","publication_status":"published","_id":"19565","title":"Multivariate Gini-type discrepancies","intvolume":"        35","oa":1,"arxiv":1,"OA_type":"green","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2411.01052"}],"year":"2025","abstract":[{"text":"Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between two multivariate distributions, we introduce a new measure of discrepancy which is scale invariant and which, in the case of two independent copies of the same distribution, and after normalization, coincides with the scaling invariant multidimensional version of the Gini index recently proposed in [P. Giudici, E. Raffinetti and G. Toscani, Measuring multidimensional inequality: A new proposal based on the Fourier transform, preprint (2024), arXiv:2401.14012 ]. A byproduct of the analysis is an easy-to-handle discrepancy metric, obtained by application of the theory to a pair of Gaussian multidimensional densities. The obtained metric does improve the standard metrics, based on the mean squared error, as it is scale invariant. The importance of this theoretical finding is illustrated by means of a real problem that concerns measuring the importance of Environmental, Social and Governance factors for the growth of small and medium enterprises. ","lang":"eng"}],"external_id":{"arxiv":["2411.01052"],"isi":["001456337300001"]},"publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"publisher":"World Scientific Publishing"},{"oa_version":"Published Version","_id":"10575","publication_status":"published","title":"On the dynamic slip boundary condition for Navier-Stokes-like problems","intvolume":"        31","oa":1,"arxiv":1,"year":"2021","abstract":[{"text":"The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting.","lang":"eng"}],"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and dispersion in nonlinear partial differential equations","grant_number":"W1245","call_identifier":"FWF"}],"tmp":{"short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"external_id":{"arxiv":["2009.09057"],"isi":["000722309400001"]},"publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"publisher":"World Scientific Publishing","type":"journal_article","issue":"11","department":[{"_id":"JuFi"}],"has_accepted_license":"1","date_updated":"2025-04-15T08:31:30Z","date_published":"2021-10-13T00:00:00Z","ddc":["510"],"month":"10","publication":"Mathematical Models and Methods in Applied Sciences","status":"public","page":"2165-2212","author":[{"first_name":"Anna","last_name":"Abbatiello","full_name":"Abbatiello, Anna"},{"full_name":"Bulíček, Miroslav","first_name":"Miroslav","last_name":"Bulíček"},{"full_name":"Maringová, Erika","last_name":"Maringová","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","first_name":"Erika"}],"language":[{"iso":"eng"}],"day":"13","date_created":"2021-12-26T23:01:27Z","file_date_updated":"2022-05-16T10:55:45Z","article_type":"original","acknowledgement":"The research of A. Abbatiello is supported by Einstein Foundation, Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No. 20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian Science Fund (FWF), grants P30000, W1245, and F65.","scopus_import":"1","file":[{"success":1,"file_name":"2021_MathModelsMethods_Abbatiello.pdf","relation":"main_file","access_level":"open_access","date_created":"2022-05-16T10:55:45Z","file_size":795483,"content_type":"application/pdf","file_id":"11385","date_updated":"2022-05-16T10:55:45Z","checksum":"8c0a9396335f0b70e1f5cbfe450a987a","creator":"dernst"}],"article_processing_charge":"No","isi":1,"citation":{"short":"A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods in Applied Sciences 31 (2021) 2165–2212.","ista":"Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 31(11), 2165–2212.","ieee":"A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary condition for Navier-Stokes-like problems,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212, 2021.","ama":"Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition for Navier-Stokes-like problems. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;31(11):2165-2212. doi:<a href=\"https://doi.org/10.1142/S0218202521500470\">10.1142/S0218202521500470</a>","apa":"Abbatiello, A., Bulíček, M., &#38; Maringová, E. (2021). On the dynamic slip boundary condition for Navier-Stokes-like problems. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202521500470\">https://doi.org/10.1142/S0218202521500470</a>","mla":"Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:<a href=\"https://doi.org/10.1142/S0218202521500470\">10.1142/S0218202521500470</a>.","chicago":"Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/S0218202521500470\">https://doi.org/10.1142/S0218202521500470</a>."},"quality_controlled":"1","volume":31,"doi":"10.1142/S0218202521500470","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"publisher":"World Scientific Publishing","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"external_id":{"isi":["000722222900004"],"arxiv":["2009.06917"]},"publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"arxiv":1,"main_file_link":[{"url":"https://arxiv.org/abs/2009.06917","open_access":"1"}],"year":"2021","abstract":[{"text":"We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.","lang":"eng"}],"keyword":["Nonlinear parabolic systems","implicit constitutive theory","weak solutions","existence","uniqueness"],"oa_version":"Preprint","_id":"10005","publication_status":"published","title":"On nonlinear problems of parabolic type with implicit constitutive equations involving flux","intvolume":"        31","oa":1,"quality_controlled":"1","citation":{"ama":"Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;31(09). doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>","apa":"Bulíček, M., Maringová, E., &#38; Málek, J. (2021). On nonlinear problems of parabolic type with implicit constitutive equations involving flux. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>","mla":"Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 09, World Scientific Publishing, 2021, doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>.","chicago":"Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>.","ista":"Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 31(09).","short":"M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied Sciences 31 (2021).","ieee":"M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic type with implicit constitutive equations involving flux,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 09. World Scientific Publishing, 2021."},"volume":31,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1142/S0218202521500457","scopus_import":"1","article_processing_charge":"No","isi":1,"author":[{"last_name":"Bulíček","first_name":"Miroslav","full_name":"Bulíček, Miroslav"},{"full_name":"Maringová, Erika","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","first_name":"Erika"},{"last_name":"Málek","first_name":"Josef","full_name":"Málek, Josef"}],"date_created":"2021-09-12T22:01:25Z","language":[{"iso":"eng"}],"day":"25","article_type":"original","acknowledgement":"M. Bulíček and J. Málek acknowledge the support of the project No. 18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers of the Nečas Center for Mathematical Modelling.\r\n","type":"journal_article","issue":"09","department":[{"_id":"JuFi"}],"date_updated":"2026-08-18T07:47:39Z","date_published":"2021-08-25T00:00:00Z","month":"08","publication":"Mathematical Models and Methods in Applied Sciences","status":"public"}]