[{"publisher":"World Scientific","publication":"Mathematical Models and Methods in Applied Sciences","month":"08","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","isi":1,"keyword":["Nonlinear parabolic systems","implicit constitutive theory","weak solutions","existence","uniqueness"],"oa":1,"author":[{"last_name":"Bulíček","first_name":"Miroslav","full_name":"Bulíček, Miroslav"},{"id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","last_name":"Maringová","first_name":"Erika","full_name":"Maringová, Erika"},{"last_name":"Málek","first_name":"Josef","full_name":"Málek, Josef"}],"external_id":{"arxiv":["2009.06917"],"isi":["000722222900004"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_published":"2021-08-25T00:00:00Z","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"year":"2021","date_updated":"2023-09-04T11:43:45Z","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"publication_status":"published","arxiv":1,"_id":"10005","main_file_link":[{"url":"https://arxiv.org/abs/2009.06917","open_access":"1"}],"citation":{"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, 2021, doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>.","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>","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, 2021.","short":"M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied Sciences 31 (2021).","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).","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. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/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, 2021. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>."},"type":"journal_article","day":"25","doi":"10.1142/S0218202521500457","quality_controlled":"1","oa_version":"Preprint","intvolume":"        31","article_type":"original","issue":"09","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"}],"volume":31,"title":"On nonlinear problems of parabolic type with implicit constitutive equations involving flux","scopus_import":"1","department":[{"_id":"JuFi"}],"language":[{"iso":"eng"}],"date_created":"2021-09-12T22:01:25Z"},{"volume":31,"tmp":{"image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"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"}],"intvolume":"        31","article_type":"original","issue":"11","department":[{"_id":"JuFi"}],"language":[{"iso":"eng"}],"date_created":"2021-12-26T23:01:27Z","title":"On the dynamic slip boundary condition for Navier-Stokes-like problems","scopus_import":"1","citation":{"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>.","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>","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.","short":"A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods in Applied Sciences 31 (2021) 2165–2212.","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>.","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>","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."},"day":"13","type":"journal_article","oa_version":"Published Version","quality_controlled":"1","doi":"10.1142/S0218202521500470","article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"2165-2212","status":"public","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","ddc":["510"],"date_published":"2021-10-13T00:00:00Z","year":"2021","publication_identifier":{"issn":["0218-2025"],"eissn":["1793-6314"]},"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.","isi":1,"author":[{"last_name":"Abbatiello","full_name":"Abbatiello, Anna","first_name":"Anna"},{"last_name":"Bulíček","first_name":"Miroslav","full_name":"Bulíček, Miroslav"},{"full_name":"Maringová, Erika","first_name":"Erika","last_name":"Maringová","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4"}],"oa":1,"external_id":{"isi":["000722309400001"],"arxiv":["2009.09057"]},"_id":"10575","arxiv":1,"date_updated":"2023-08-17T06:29:01Z","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"publication_status":"published","file_date_updated":"2022-05-16T10:55:45Z","has_accepted_license":"1","publisher":"World Scientific Publishing","month":"10","file":[{"content_type":"application/pdf","relation":"main_file","success":1,"file_size":795483,"checksum":"8c0a9396335f0b70e1f5cbfe450a987a","file_name":"2021_MathModelsMethods_Abbatiello.pdf","date_created":"2022-05-16T10:55:45Z","file_id":"11385","access_level":"open_access","creator":"dernst","date_updated":"2022-05-16T10:55:45Z"}],"publication":"Mathematical Models and Methods in Applied Sciences"}]