Global solutions and blow up solutions to a class of pseudo-parabolic equations with nonlocal term

Xiaoli Zhu, Fuyi Li and Yuhua Li

Applied Mathematics and Computation, 2018, vol. 329, issue C, 38-51

Abstract: In this paper, we investigate an initial boundary value problem to a class of pseudo-parabolic partial differential equations with Newtonian nonlocal term. First, the local existence and uniqueness of a weak solution is established. In virtue of the energy functional and the related Nehari manifold, we also describe the exponent decay behavior and the blow up phenomenon of weak solutions with different kinds of initial data. Our second conclusion states that some solutions starting in a potential well exist globally, whereas solutions with suitable initial data outside the potential well must blow up. Furthermore, the instability of a ground state equilibrium solution is studied.

Keywords: Pseudo-parabolic equation; Newtonian nonlocal term; Potential well; Global weak solution; Blow up (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:329:y:2018:i:c:p:38-51

DOI: 10.1016/j.amc.2018.02.003

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