A class of fourth-order dispersive wave equations with exponential source

IF 2.1 2区数学 Q1 MATHEMATICS Calculus of Variations and Partial Differential Equations Pub Date : 2024-05-05 DOI:10.1007/s00526-024-02731-7

Tran Quang Minh, Hong-Danh Pham, Mirelson M. Freitas

引用次数: 0

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.

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本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Calculus of Variations and Partial Differential Equations 数学-数学

CiteScore

3.30

自引率

4.80%

发文量

224

审稿时长

6 months

期刊介绍： Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives. This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.