一类带非齐次记忆项抛物方程解的整体存在性和爆破
Global Existence and Blow-up for a Class of Parabolic Equations with Nonhomogeneous Memory Terms
王政慧 1祝雪 1杨晗1
作者信息
- 1. 西南交通大学 数学学院,四川 成都 611756
- 折叠
摘要
该文研究一类带非齐次记忆项抛物方程的柯西问题,讨论非线性项和非齐次项对整体解存在性的影响.当非线性项指数增长高于某一值时,利用压缩映射原理,证明了整体解的存在唯一性;当非线性项指数增长低于某一值时,利用测试函数法,证明了解在有限时刻爆破.
Abstract
The purpose of this paper is to study the Cauchy problem for a class of parabolic equations with non-homogeneous memo-ry term.This paper investigates the influence of nonlinear and non-homogeneous terms on the existence of global solutions.When the exponential growth of the nonlinear term is higher than a certain number,the existence and uniqueness of the global solution are proved by using the contraction mapping principle.Using the test function method,this paper proves that the solution blows up in fi-nite time when the exponential growth of the nonlinear term is lower than a certain number.
关键词
柯西问题/压缩映射原理/测试函数法/整体解/爆破Key words
Cauchy problem/contraction mapping principle/test function method/global existence/Blow-up引用本文复制引用
基金项目
国家自然科学基金(11701477)
国家自然科学基金(11971394)
出版年
2024
国家科技期刊平台
NSTL
万方数据