Global Solutions and Blow-Up for the Wave Equation with Variable Coefficients: I. Interior Supercritical Source

Tae Gab Ha

doi:10.1007/s00245-021-09785-5

Global Solutions and Blow-Up for the Wave Equation with Variable Coefficients: I. Interior Supercritical Source

Tae Gab Ha^*

^*Corresponding author for this work

Department of Mathematics

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

4 Scopus citations

Abstract

In this paper, we consider the variable coefficient wave equation with damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy.

Original language	English
Pages (from-to)	767-803
Number of pages	37
Journal	Applied Mathematics and Optimization
Volume	84
DOIs	https://doi.org/10.1007/s00245-021-09785-5
State	Published - 2021.12

Keywords

Blow-up
Energy decay rates
Existence of solutions
supercritical source
Wave equation with variable coefficients

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1007/s00245-021-09785-5

Cite this

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title = "Global Solutions and Blow-Up for the Wave Equation with Variable Coefficients: I. Interior Supercritical Source",

abstract = "In this paper, we consider the variable coefficient wave equation with damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy.",

keywords = "Blow-up, Energy decay rates, Existence of solutions, supercritical source, Wave equation with variable coefficients",

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

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2021",

month = dec,

doi = "10.1007/s00245-021-09785-5",

language = "English",

volume = "84",

pages = "767--803",

journal = "Applied Mathematics and Optimization",

issn = "0095-4616",

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TY - JOUR

T1 - Global Solutions and Blow-Up for the Wave Equation with Variable Coefficients

T2 - I. Interior Supercritical Source

AU - Ha, Tae Gab

PY - 2021/12

Y1 - 2021/12

N2 - In this paper, we consider the variable coefficient wave equation with damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy.

AB - In this paper, we consider the variable coefficient wave equation with damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy depending on the growth near zero on the damping term. Moreover, we prove the blow-up of the weak solution with positive initial energy as well as nonpositive initial energy.

KW - Blow-up

KW - Energy decay rates

KW - Existence of solutions

KW - supercritical source

KW - Wave equation with variable coefficients

UR - https://www.scopus.com/pages/publications/85106334796

U2 - 10.1007/s00245-021-09785-5

DO - 10.1007/s00245-021-09785-5

M3 - Journal article

AN - SCOPUS:85106334796

SN - 0095-4616

VL - 84

SP - 767

EP - 803

JO - Applied Mathematics and Optimization

JF - Applied Mathematics and Optimization

ER -

Global Solutions and Blow-Up for the Wave Equation with Variable Coefficients: I. Interior Supercritical Source

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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