Abstract
We consider a system consisting of a quasilinear parabolic equation and a first order ordinary differential equation where both equations contain functional dependence on the unknown functions. Then we consider a system which consists of a quasilinear parabolic partial differential equation, a first order ordinary differential equation and an elliptic partial differential equation. These systems were motivated by models describing diffusion and transport in porous media with variable porosity.
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Dedicated to the memory of Professor Miklós Farkas
Supported by the Hungarian NFSR under grant OTKA T 049819.
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Simon, L. On nonlinear systems consisting of different types of differential equations. Period Math Hung 56, 143–156 (2008). https://doi.org/10.1007/s10998-008-5143-3
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DOI: https://doi.org/10.1007/s10998-008-5143-3