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Communications on Pure and Applied Analysis (CPAA)
 

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

Pages: 2465 - 2485, Volume 14, Issue 6, November 2015      doi:10.3934/cpaa.2015.14.2465

 
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Xiaoli Zhu - School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China (email)
Fuyi Li - School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China (email)
Ting Rong - School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China (email)

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.

Keywords:  Pseudo-parabolic equation, global existence, blow up, potential wells, sufficient condition
Mathematics Subject Classification:  35K70, 35A01, 35B44

Received: June 2015;      Revised: August 2015;      Available Online: September 2015.

 References