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Nonlocal approximation of an anisotropic cross-diffusion system
Tomasz Dębiec, Markus Schmidtchen
Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems.…
Stability of solutions of the porous medium equation with growth with respect to the diffusion exponent
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +1
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between…
A tribute to conservation of energy for weak solutions
Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolu…