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math.AP2024
Nonlocal-to-local convergence of the Cahn-Hilliard equation with degenerate mobility and the Flory-Huggins potential
Charles Elbar, Jakub Skrzeczkowski
The Cahn-Hilliard equation is a fundamental model for phase separation phenomena. Its rigorous derivation from the nonlocal aggregation equation, motivated by the desire to link in…
math.AP2022
Non-Newtonian fluids with discontinuous-in-time stress tensor
Miroslav Buliček, Piotr Gwiazda, Jakub Skrzeczkowski +1
We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and ha…
math.AP2021
Measure Differential Equation with a Nonlinear Growth/Decay Term
Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra +1
We obtain an existence result for a Measure Differential Equation with an additional nonlinear growth/decay term that may change the sign. The proof requires a modification of appr…