山西大学学报（自然科学版）2024，Vol.47Issue(5)：901-911,11.DOI:10.13451/j.sxu.ns.2023156
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
摘要
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分类
数理科学引用本文复制引用
王政慧,祝雪,杨晗..一类带非齐次记忆项抛物方程解的整体存在性和爆破[J].山西大学学报（自然科学版）,2024,47(5):901-911,11.基金项目
国家自然科学基金(11701477 （）
11971394) （）
