GLOBAL SOLUTIONS AND BLOW-UP FOR WAVE EQUATIONS WITH VARIABLE COEFFICIENTS AND BOUNDARY SUPERCRITICAL SOURCE

Tae Gab Ha

doi:10.58997/ejde.2025.104

GLOBAL SOLUTIONS AND BLOW-UP FOR WAVE EQUATIONS WITH VARIABLE COEFFICIENTS AND BOUNDARY SUPERCRITICAL SOURCE

Tae Gab Ha^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

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.

Original language	English
Article number	104
Journal	Electronic Journal of Differential Equations
Volume	2025
DOIs	https://doi.org/10.58997/ejde.2025.104
State	Published - 2025

Keywords

Wave equation with variable coefficients
blow-up
energy decay rates
existence of solutions
supercritical source

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10.58997/ejde.2025.104

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title = "GLOBAL SOLUTIONS AND BLOW-UP FOR WAVE EQUATIONS WITH VARIABLE COEFFICIENTS AND BOUNDARY SUPERCRITICAL SOURCE",

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.",

keywords = "Wave equation with variable coefficients, blow-up, energy decay rates, existence of solutions, supercritical source",

author = "Ha, \{Tae Gab\}",

year = "2025",

doi = "10.58997/ejde.2025.104",

language = "English",

volume = "2025",

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TY - JOUR

T1 - GLOBAL SOLUTIONS AND BLOW-UP FOR WAVE EQUATIONS WITH VARIABLE COEFFICIENTS AND BOUNDARY SUPERCRITICAL SOURCE

AU - Ha, Tae Gab

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Wave equation with variable coefficients

KW - blow-up

KW - energy decay rates

KW - existence of solutions

KW - supercritical source

UR - https://www.scopus.com/pages/publications/105022737865

U2 - 10.58997/ejde.2025.104

DO - 10.58997/ejde.2025.104

M3 - Journal article

AN - SCOPUS:105022737865

SN - 1550-6150

VL - 2025

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

M1 - 104

ER -

GLOBAL SOLUTIONS AND BLOW-UP FOR WAVE EQUATIONS WITH VARIABLE COEFFICIENTS AND BOUNDARY SUPERCRITICAL SOURCE

Abstract

Keywords

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