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arXiv · 2606.05879

Convergence of a discrete-in-time Approximation to a Degenerate Parabolic-Hyperbolic System

Julia Hauser·Hideki Murakawa·Markus Schmidtchen
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Abstract

In this paper we consider an implicit semi-discrete approximation of a degenerate reaction-cross-diffusion system. Due to the symmetry in the parabolic part, this system is known to preserve segregation of densities -- initially non-overlapping densities belonging to different species remain segregated for all times, which leads to internal layers between different species. We show that time-discrete approximations exist and converge to a weak solution, as the timestep goes to zero.

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Julia Hauser, Hideki Murakawa, Markus Schmidtchen. 2026-06-04. Convergence of a discrete-in-time Approximation to a Degenerate Parabolic-Hyperbolic System. https://arxiv.org/abs/2606.05879

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