具有记忆项和广义Lewis函数的Kirchhoff型抛物方程解的一致衰减估计和爆破
General Decay and Blow Up of Solution for an Kirchhoff Parabolic Equation with a Memory Term and a Generalized Lewis Function
史清方 1张新丽1
作者信息
- 1. 青岛科技大学 数理学院,山东 青岛 266061
- 折叠
摘要
研究具有混合边界条件和广义Lewis函数的一类半线性抛物型方程的衰减和爆破性质.首先,通过引进简单的Lyapunov函数和严密的先验估计值方法得到能量的一致衰减估计值,其中包括指数和代数衰减两种情形.其次,通过修正的凹性方法得到当初始值具有适当的负能量时,解在有限时间内爆炸,并给出了解的生命跨度的精确估计.
Abstract
In this paper,we consider the decay and blow up properties of a semi-linear para-bolic equation with a mixed boundary condition and a generalized Lewis functions.Under suitable conditions,we firstly establish a general decay result,from which the usual expo-nential and polynomial decay results are only special cases.Then we prove the solution blows up in finite time if the initial datum possesses suitable negative energy by the modifi-fied concavity method.Moreover,we have a precise estimate for the lifespan of the solution in this case.
关键词
记忆项/广义Lewis函数/混合边值问题/一致衰减/爆破Key words
memory term/generalized Lewis function/mixed boundary value problems/gnearal decay/blow up引用本文复制引用
基金项目
山东省自然科学基金(ZR2023QA008)
出版年
2024
NETL
NSTL
万方数据