EXISTENCE OF SIGN-CHANGING SOLUTIONS FOR THE H<acute accent>ENON TYPE PARABOLIC EQUATION WITH SINGULAR INITIAL DATA

被引：0
|
作者：
Geng, Qiuping [1 ]
Wang, Jun [1 ]
机构：
[1] Jiangsu Univ, Sch Math Sci, Zhenjiang 212013, Jiangsu, Peoples R China
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2024年 / 23卷 / 02期
基金：
中国国家自然科学基金; 国家重点研发计划;
关键词：
Self-similar solutions; sign-changing solutions; He ' non type parabolic equation; related inverted profile equation; initial value; NONLINEAR HEAT-EQUATION; SELF-SIMILAR SOLUTIONS; LARGE TIME BEHAVIOR; GLOBAL-SOLUTIONS; CAUCHY-PROBLEM; NONEXISTENCE; NONUNIQUENESS; UNIQUENESS;
D O I：
10.3934/cpaa.2024005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, we study the H enon type parabolic equation phi(t)-triangle phi=|x|(beta)|phi|(alpha-1)phi,x is an element of R(N )with singular initial data eta|x|(-2+beta/alpha-1), where eta,beta >0,alpha >1. We prove the existence of infinitely many sign-changing self-similar solutions by analyzing the related inverted profile equation for N >= 1.This can be seen as an extension of the recent work of T. Cazenave at al.(Amer.J. Math. 142 (2020), 1439-1495) to the H enon type parabolic equation.
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页码：165 / 194
页数：30
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