The Blow-Up of the Local Energy Solution to the Wave Equation with a Nontrivial Boundary Condition

Author:

Liu Yulong1ORCID

Affiliation:

1. School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, China

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.

Funder

Shanxi Province Higher Edution Science and Technology Innovation Project

Publisher

MDPI AG

Reference28 articles.

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