The Stability of Small Stationary Solutions in Morrey Spaces of the Semilinear Heat Equations

Journal of Mathematical Sciences

Xiaofang, Zhou¹ 

关键词: Morrey spaces;    stability;    semilinear heat equations;    stationary solutions;    semigroup operator;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Inthispaper,weconsiderinMorreyspacestheCauchyproblemofthesemilinearheatequationwithanexternalforce.Underappropriateassumptionsontheexternalforce,weprovedtheuniqueexistenceofsmallsolutiontothecorrespondingstationaryproblem.Moreover,iftheinitialdataiscloseenoughtothestationarysolution,weverifiedthetime-globalsolvabilityoftheCauchyproblem,whichleadstothestabilityofthesmallstationarysolution.

【 授权许可】

Unknown