Global well-posedness of semilinear hyperbolic equations, parabolic equations and Schrodinger equations

This article studies the existence and nonexistence of global solutions to the initial boundary value problems for semilinear wave and heat equation, and for Cauchy problem of nonlinear Schrodinger equation. This is done under three possible initial energy levels, except the NLS as it does not have...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2018; no. 55; pp. 1 - 52
Main Authors Runzhang Xu, Yuxuan Chen, Yanbing Yang, Shaohua Chen, Jihong Shen
Format Journal Article
LanguageEnglish
Published Texas State University 23.02.2018
Subjects
global solution
nonlinear Schrodinger equation
potential well
Semilinear hyperbolic equation
semilinear parabolic equation
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Summary:This article studies the existence and nonexistence of global solutions to the initial boundary value problems for semilinear wave and heat equation, and for Cauchy problem of nonlinear Schrodinger equation. This is done under three possible initial energy levels, except the NLS as it does not have comparison principle. The most important feature in this article is a new hypothesis on the nonlinear source terms which can include at least eight important and popular power-type nonlinearities as special cases. This article also finds some kinds of divisions for the initial data to guarantee the global existence or finite time blowup of the solution of the above three problems.
ISSN:1072-6691
1072-6691