Time periodic solution to a mechanochemical model in biological patterns

Chengxin Du; Changchun Liu

doi:10.3934/eect.2022039

Article Contents

2023, Volume 12, Issue 2: 502-524. Doi: 10.3934/eect.2022039

This issue Previous Article Controllability of a simplified time-discrete stabilized Kuramoto-Sivashinsky system Next Article Controllability of fractional measure evolution systems with state-dependent delay and nonlocal condition

Time periodic solution to a mechanochemical model in biological patterns

Chengxin Du and
Changchun Liu^,

Department of Mathematics, Jilin University, Changchun 130012, China

^*Corresponding author: Changchun Liu
^*Corresponding author: Changchun Liu

Received: May 2022

Revised: July 2022

Early access: August 2022

Published: April 2023

This work is supported by the Jilin Scientific and Technological Development Program (no. 20210101466JC).

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Abstract

In this paper, we consider a mechanochemical model in biological patterns in $ \mathbb{R}^N $, $ N\geq 5 $. We first prove the existence of time periodic solution in $ BC(\mathbb{R}; L^{N,\infty}(\Omega)) $. Then we obtain the existence, uniqueness and regularity of the mild solution of the problem. Finally, we prove that the mild solution can become strong solution in $ BC(\mathbb{R}; L^{N,\infty}(\Omega)) $.

Keywords:

Mechanochemical model in biological patterns,
time periodic solution,
mild solution,
integral equation.

Mathematics Subject Classification: Primary: 35B10, 35K41; Secondary: 92C15, 45G15.

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