Electron. J. Differential Equations, Vol. 2025 (2025), No. 104, pp. 1-31.

Global solutions and blow-up for wave equations with variable coefficients and boundary supercritical source

Tae Gab Ha

Abstract:
In this study, we consider a wave equation with variable coefficients, boundary damping, and supercritical source terms. This study aims to study the local and global existence and classify the decay rate of energy depending on the growth near zero in the damping term. Furthermore, we demonstrate that the weak solution blows up in finite time with positive and nonpositive initial energies.

Submitted June 5, 2025. Published November 4, 2025
Math Subject Classifications: 35L05, 35L20, 35A01, 35B40, 35B44.
Key Words: Wave equation with variable coefficients; supercritical source; blow-up; existence of solutions; energy decay rates.
DOI: 10.58997/ejde.2025.104

Show me the PDF file (552 KB), TEX file for this article.

Tae Gab Ha
Department of Mathematics
and Institute of Pure and Applied Mathematics
Jeonbuk National University
Jeonju 54896, Korea
email: tgha@jbnu.ac.kr

Return to the EJDE web page