The Well-Posedness of Solution to Semilinear Pseudo-parabolic Equation

In this paper, we use the Green’s function method to get the pointwise convergence rate of the semilinear pseudo-parabolic equations. By using this precise pointwise structure and introducing negative index Sobolev space condition on the initial data, we release the critical index of the nonlinearit...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 35; no. 2; pp. 386 - 400
Main Authors Wang, Wei-ke, Wang, Yu-tong
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2019
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinearity
Sobolev space
Theoretical
Well posed problems
pointwise
negative index Sobolev space
Green’s function
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Summary:In this paper, we use the Green’s function method to get the pointwise convergence rate of the semilinear pseudo-parabolic equations. By using this precise pointwise structure and introducing negative index Sobolev space condition on the initial data, we release the critical index of the nonlinearity for blowing up. Our result shows that the global existence does not only depend on the nonlinearity but also the initial condition.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-019-0817-7