BLOW-UP AND LIFESPAN ESTIMATE FOR WAVE EQUATIONS WITH CRITICAL DAMPING TERM OF SPACE-DEPENDENT TYPE RELATED TO GLASSEY CONJECTURE

Ahmad Z. Fino; Mohamed Ali Hamza

doi:10.3934/dcdss.2022192

BLOW-UP AND LIFESPAN ESTIMATE FOR WAVE EQUATIONS WITH CRITICAL DAMPING TERM OF SPACE-DEPENDENT TYPE RELATED TO GLASSEY CONJECTURE

Ahmad Z. Fino
, Mohamed Ali Hamza^*

^*Corresponding author for this work

Department of Basic Sciences

American University of the Middle East

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The main purpose of the present paper is to study the blow-up problem of the wave equation with space-dependent damping in the scale-invariant case and time derivative nonlinearity with small initial data. Under appropriate initial data which are compactly supported, by using a test function method and taking into account the effect of the damping term (Formula Presented), we show that in higher dimensions the blow-up region is given by p ∈ (1, p_G(N + µ)] where p_G(N) is the Glassey exponent. Furthermore, we shall establish a blow-up region, independent of µ given by (Formula Presented), for appropriate initial data in the energy space with noncompact support.

Original language	English
Pages (from-to)	1383-1400
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	16
Issue number	6
DOIs	https://doi.org/10.3934/dcdss.2022192
State	Published - 2023

Keywords

Blow-up
lifespan
nonlinear wave equations
scale-invariant damping
time-derivative nonlinearity

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10.3934/dcdss.2022192

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title = "BLOW-UP AND LIFESPAN ESTIMATE FOR WAVE EQUATIONS WITH CRITICAL DAMPING TERM OF SPACE-DEPENDENT TYPE RELATED TO GLASSEY CONJECTURE",

abstract = "The main purpose of the present paper is to study the blow-up problem of the wave equation with space-dependent damping in the scale-invariant case and time derivative nonlinearity with small initial data. Under appropriate initial data which are compactly supported, by using a test function method and taking into account the effect of the damping term (Formula Presented), we show that in higher dimensions the blow-up region is given by p ∈ (1, pG(N + µ)] where pG(N) is the Glassey exponent. Furthermore, we shall establish a blow-up region, independent of µ given by (Formula Presented), for appropriate initial data in the energy space with noncompact support.",

keywords = "Blow-up, lifespan, nonlinear wave equations, scale-invariant damping, time-derivative nonlinearity",

author = "Fino, \{Ahmad Z.\} and Hamza, \{Mohamed Ali\}",

year = "2023",

doi = "10.3934/dcdss.2022192",

language = "English",

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pages = "1383--1400",

journal = "Discrete and Continuous Dynamical Systems - Series S",

issn = "1937-1632",

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T1 - BLOW-UP AND LIFESPAN ESTIMATE FOR WAVE EQUATIONS WITH CRITICAL DAMPING TERM OF SPACE-DEPENDENT TYPE RELATED TO GLASSEY CONJECTURE

AU - Fino, Ahmad Z.

AU - Hamza, Mohamed Ali

PY - 2023

Y1 - 2023

N2 - The main purpose of the present paper is to study the blow-up problem of the wave equation with space-dependent damping in the scale-invariant case and time derivative nonlinearity with small initial data. Under appropriate initial data which are compactly supported, by using a test function method and taking into account the effect of the damping term (Formula Presented), we show that in higher dimensions the blow-up region is given by p ∈ (1, pG(N + µ)] where pG(N) is the Glassey exponent. Furthermore, we shall establish a blow-up region, independent of µ given by (Formula Presented), for appropriate initial data in the energy space with noncompact support.

AB - The main purpose of the present paper is to study the blow-up problem of the wave equation with space-dependent damping in the scale-invariant case and time derivative nonlinearity with small initial data. Under appropriate initial data which are compactly supported, by using a test function method and taking into account the effect of the damping term (Formula Presented), we show that in higher dimensions the blow-up region is given by p ∈ (1, pG(N + µ)] where pG(N) is the Glassey exponent. Furthermore, we shall establish a blow-up region, independent of µ given by (Formula Presented), for appropriate initial data in the energy space with noncompact support.

KW - Blow-up

KW - lifespan

KW - nonlinear wave equations

KW - scale-invariant damping

KW - time-derivative nonlinearity

UR - https://www.scopus.com/pages/publications/85163534287

U2 - 10.3934/dcdss.2022192

DO - 10.3934/dcdss.2022192

M3 - Article

AN - SCOPUS:85163534287

SN - 1937-1632

VL - 16

SP - 1383

EP - 1400

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 6

ER -

BLOW-UP AND LIFESPAN ESTIMATE FOR WAVE EQUATIONS WITH CRITICAL DAMPING TERM OF SPACE-DEPENDENT TYPE RELATED TO GLASSEY CONJECTURE

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