Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity

We consider the initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity. Constructing a family of potential wells and using the logarithmic Sobolev inequality, we establish the existence of global weak solutions. we consider two cases: glob...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2018; no. 116; pp. 1 - 19
Main Authors Yang Cao, Conghui Liu
Format Journal Article
LanguageEnglish
Published Texas State University 14.05.2018
Subjects
logarithmic nonlinearity
long time behavior
p-Laplacian
Pseudo-parabolic
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ISSN1072-6691

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Summary:We consider the initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity. Constructing a family of potential wells and using the logarithmic Sobolev inequality, we establish the existence of global weak solutions. we consider two cases: global boundedness and blowing-up at infinity. Moreover, we discuss the asymptotic behavior of solutions and give some decay estimates and growth estimates.
ISSN:1072-6691