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

作　　者：王政慧 祝雪 杨晗[1] WANG Zhenghui;ZHU Xue;YANG Han(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《山西大学学报（自然科学版）》2024年第5期901-911,共11页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11701477,11971394)。

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。The purpose of this paper is to study the Cauchy problem for a class of parabolic equations with non-homogeneous memory 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 finite 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 

分 类 号：O175.29[理学—数学]