On nonlinear problems of parabolic type with implicit constitutive equations involving flux

@article{Bulivcek2021OnNP,
  title={On nonlinear problems of parabolic type with implicit constitutive equations involving flux},
  author={Miroslav Bul'ivcek and Josef M'alek and Erika Maringov'a},
  journal={Mathematical Models and Methods in Applied Sciences},
  year={2021}
}
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… 
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