Formulation of Chimera Gradient Flows for Chemotaxis Systems with Indirect Signal Production and Degenerate Diffusion
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 timediscrete approximate solution. Unlike standard minimizing movement scheme for gradient flows, the relative compactness of the timediscrete 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 timeglobal solutions.
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.14536
 arXiv:
 arXiv:2406.14536
 Bibcode:
 2024arXiv240614536M
 Keywords:

 Mathematics  Analysis of PDEs