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math.AP2026
The Cauchy Problem For Quasi-Linear Parabolic Systems Revisited
Isabelle Gallagher, Ayman Moussa
We study a class of parabolic quasilinear systems, in which the diffusion matrix is not uniformly elliptic, but satisfies a Petrovskii condition of positivity of the real part of t…
math.AP2025
Stability of non-conservative cross diffusion model and approximation by stochastic particle systems
Vincent Bansaye, Alexandre Bertolino, Ayman Moussa
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become loc…