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- Title
A class of fourth-order dispersive wave equations with exponential source.
- Authors
Minh, Tran Quang; Pham, Hong-Danh; Freitas, Mirelson M.
- Abstract
This paper is concerned with a class of fourth-order dispersive wave equations with exponential source term. Firstly, by applying the contraction mapping principle, we establish the local existence and uniqueness of the solution. In the spirit of the variational principle and mountain pass theorem, a natural phase space is precisely divided into three different energy levels. Then we introduce a family of potential wells to derive a threshold of the existence of global solutions and blow up in finite time of solution in both cases with sub-critical and critical initial energy. These results can be used to extend the previous result obtained by Alves and Cavalcanti (Calc. Var. Partial Differ. Equ. 34 (2009) 377–411). Moreover, an explicit sufficient condition for initial data leading to blow up result is established at an arbitrarily positive initial energy level.
- Subjects
BLOWING up (Algebraic geometry); MOUNTAIN pass theorem; PHASE space; VARIATIONAL principles; THRESHOLD energy; WAVE equation; POTENTIAL well
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 5, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-024-02731-7