Formulation of Chimera Gradient Flows for Chemotaxis Systems with Indirect Signal Production and Degenerate Diffusion

2024/06/20 by Yoshifumi Mimura, Mimura, Yoshifumi
Engineering · Mathematics · #3D Printing in Biomedical Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.2406.14536

openalex publication_date 2024/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A parabolic system of three unknown functions, not expressible as gradient flows, is treated as three coupled gradient flows. For each unknown function, the minimizing movement scheme is used to construct a time-discrete approximate solution. Unlike standard minimizing movement scheme for gradient flows, the relative compactness of the time-discrete approximate solution with respect to the time step is not inherently guaranteed. However, the existence of a Lyapunov functional ensures this relative compactness, leading to the existence of time-global solutions.

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