Abstract:The system of multispecies chemotaxis equations is a cross-diffusion system with volume-filling. In this work, we show that a weak solution of the two species chemotaxis system exists. The entropy method is a major tool in existence analysis of cross-diffusion systems. Previous investigations indicate that traditional entropies in volume-filling cases may not be able to provide required gradient estimates. In this situation, we upgrade existing matrix computation methods to derive gradient estimates. Due to the cross-diffusion phenomenon, the uniqueness of the weak solution to a cross-diffusion system is very difficult to prove in general. In this work, we apply the distance functional to show that when parameters of the chemotaxis system are identical, the weak solution is unique.
From: Xi Lin [view email]
[v1]
Tue, 18 Feb 2025 11:31:25 UTC (12 KB)
[v2]
Sun, 23 Feb 2025 15:04:10 UTC (10 KB)
[v3]
Fri, 26 Dec 2025 16:10:38 UTC (14 KB)
[v4]
Mon, 27 Apr 2026 15:46:19 UTC (15 KB)
[v5]
Mon, 14 Sep 2026 09:41:51 UTC (14 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。