A blow-up result of a free boundary problem with nonlinear advection term

被引：0

作者：

Zhang, Qianmeng ^{[1
]}

Cai, Jingjing ^{[1
]}

Xu, Li ^{[1
]}

机构：

[1] Shanghai Univ Elect Power, Sch Math & Phys, Shanghai, Peoples R China

来源：

APPLICABLE ANALYSIS | 2025年 / 104卷 / 04期

关键词：

Advection; free boundary problem; blow up; REACTION-DIFFUSION EQUATION; ASYMPTOTIC-BEHAVIOR; LOGISTIC MODEL; STEFAN PROBLEM; GLOBAL EXISTENCE; TIME BEHAVIOR;

D O I：

10.1080/00036811.2024.2376081

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a free boundary problem for the reaction-diffusion equation with nonlinear advection term ut = uxx - uux + up(p > 1) on [0, h(t)]. This model describes species that live in an uninhabitable area and tries to spread into a new area, the free boundary h(t) represents such a spreading front. By considering the initial data sf, we have two sharp results. There is some s * > 0, blow up happens whens > s *, vanishing happens when s < s * and the transition case happens when s = s *. Additionally, wealso have another trichotomy result: the solution is either blow up or converging to a small stationary state or converging to a big stationary state.

引用

页码：598 / 611

页数：14

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