Free boundary problems for the local-nonlocal diffusive model with different moving parameters

Heting Zhang; Lei Li; Mingxin Wang

doi:10.3934/dcdsb.2022085

Article Contents

2023, Volume 28, Issue 1: 474-498. Doi: 10.3934/dcdsb.2022085

This issue Previous Article A non-intrusive model order reduction approach for parameterized time-domain Maxwell's equations Next Article Smoluchowski–Kramers approximation with state dependent damping and highly random oscillation

Free boundary problems for the local-nonlocal diffusive model with different moving parameters

1.
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2.
College of Science, Henan University of Technology, Zhengzhou 450001, China
3.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

^* Corresponding author: Lei Li
^* Corresponding author: Lei Li

Received: November 30, 2021

Revised: February 28, 2022

Early access: May 2022

Published: January 2023

The work is supported by NSFC grants 12171120, 11971128

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Abstract

This paper concerns a class of local and nonlocal diffusion systems with double free boundaries possessing different moving parameters. We firstly obtain the existence, uniqueness and regularity of global solution and then prove that its dynamics are governed by a spreading-vanishing dichotomy. Then the sharp criteria for spreading and vanishing are established. Of particular importance is that long-time behaviors of solution in this problem are quite rich under the Lotka-Volterra type competition, prey-predator and mutualist growth conditions. Moreover, we also provide rough estimates of spreading speeds when spreading happens.

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Mathematics Subject Classification: Primary: 35K57, 35R20, 35R35, 92D25.

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