L
Li, Fengjie
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A Note on a Mixed Pseudo-Parabolic Kirchhoff Equation with Logarithmic Damping

Abstract

This paper deals with a homogeneous Dirichlet initial-boundary value problem of the Kirchhoff equation of pseudo-parabolic type with logarithmic nonlinearity, u(t) - Delta u(t) - M(parallel to del u parallel to(2)(2))Delta u = vertical bar u vertical bar(q-2)u log vertical bar u vertical bar, (x, t) is an element of Omega x (0, T), where M(s) := a + bs, a, b > 0, q > 2; Omega subset of R-N is a bounded domain with Lipschitz boundary. Firstly, we employ the extended Galerkin method to prove the local existence and uniqueness of weak solution. Secondly, for q > 4, we show the criteria on the existence of blow-up solutions or global solutions, which depend on the choosing of the initial energy and Nehari energy. Thirdly, for q + mu <= 4, we give the results on global solutions and large time estimate, where mu is a positive constant.

article Article
date_range 2024
language English
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L
Li Fengjie
L
Li Ping
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Featured Keywords
Kirchhoff equation
Pseudo-parabolic equation
Local existence
Blow-up time
Large time estimate
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