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

作　　者：史清方 张新丽[1] SHI Qingfang;ZHANG Xinli(College of Mathematics and Physics,Qingdao University of Science and Technology,Qingdao 266061,China)

机构地区：[1]青岛科技大学数理学院,山东青岛266061

出　　处：《青岛科技大学学报（自然科学版）》2024年第3期152-158,共7页Journal of Qingdao University of Science and Technology:Natural Science Edition

基　　金：山东省自然科学基金项目(ZR2023QA008)。

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。In this paper,we consider the decay and blow up properties of a semi-linear parabolic 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 exponential 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 modifified 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 

分 类 号：O175.1[理学—数学]