半线性抛物方程的Pohozaev恒等式及其应用  

Pohozaev Identities for the Semilinear Parabolic Equations and Applications

作　　者：冯廷福 朱艳 母贵 FENG Tingfu;ZHU Yan;MU Gui(School of Mathematics,Kunming University,Kunming 650214,China)

机构地区：[1]昆明学院数学学院,云南昆明650214

出　　处：《应用数学》2023年第3期773-779,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(12261053);the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities Association(2019FH001-078,202101BA070001-132);Introduction of Talents Research Project of Kunming University(XJ20210020,YJL20019)。

摘　　要：本文受Pohozaev(1965)的启发,利用散度定理和格林公式建立了半线性抛物方程的Pohozaev恒等式.利用这个恒等式,我们分别证明了一些半线性抛物方程和方程组在适当的条件下不存在非平凡解.我们将半线性椭圆方程的一些不存在性结果推广到半线性抛物方程.Inspired by Pohozaev(1965),we establish the Pohozaev identity for the semilinear parabolic equation by the divergence theorem and Green's formula in this paper.Using this identity,we prove that there has no nontrivial solutions for some semilinear parabolic equations and systems under suitable conditions,respectively.Our results extend some earlier nonexistence results from semilinear elliptic equations to semilinear parabolic equations.

关 键 词：半线性抛物方程 POHOZAEV恒等式 不存在性 

分 类 号：O175.29[理学—数学]