Global existence and blow up of solutions to a class of pseudo-parabolic equations with an exponential source
Xiaoli Zhu - 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
Received: June 2015; Revised: August 2015; Available Online: September 2015.
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