Global existence and blow up of solutions to a class of pseudo-parabolic equations with an exponential source

Xiaoli  Zhu; Fuyi  Li; Ting  Rong

doi:10.3934/cpaa.2015.14.2465

Article Contents

2015, Volume 14, Issue 6: 2465-2485. Doi: 10.3934/cpaa.2015.14.2465

This issue Previous Article Wellposedness of the Keller-Segel Navier-Stokes equations in the critical Besov spaces Next Article Nodal solutions for a quasilinear Schrödinger equation with critical nonlinearity and non-square diffusion

Global existence and blow up of solutions to a class of pseudo-parabolic equations with an exponential source

1.
School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi

Received: May 31, 2015

Revised: July 31, 2015

Published: October 2015

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Abstract

In this paper, a class of pseudo-parabolic equations with an exponential source is concerned. First, by the elliptic regularity theory, we establish the local existence and uniqueness of solutions. Sequently, the global existence and blow up of solutions with lower initial energy is considered via the potential wells method. Finally, we find a sufficient condition under which the solution blows up without any limit of initial energy by constructing a new functional which falls between the energy functional and Nehari functional. During this process, the properties of global solutions are also studied.

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Mathematics Subject Classification: 35K70, 35A01, 35B44.

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