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- Title
The Blow-Up of the Local Energy Solution to the Wave Equation with a Nontrivial Boundary Condition.
- Authors
Liu, Yulong
- Abstract
In this study, we examine the wave equation with a nontrivial boundary condition. The main target of this study is to prove the local-in-time existence and the blow-up in finite time of the energy solution. Through the construction of an auxiliary function and the imposition of appropriate conditions on the initial data, we establish the both lower and upper bounds for the blow-up time of the solution. Meanwhile, based on these estimates, we obtain the result of the local-in-time existence and the blow-up of the energy solution. This approach enhances our understanding of the dynamics leading to blow-up in the considered condition.
- Subjects
WAVE equation; BLOWING up (Algebraic geometry); NONLINEAR wave equations; WAVE energy; BOUNDARY value problems
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 9, p1317
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12091317