Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms

Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms

Abstract We prove the global existence of small data solution in all spaces of all dimensions n ≥ 1 $n\geq 1$ for weakly coupled systems of semilinear effectively damped wave, with different time-dependent coefficients in the dissipation terms. Moreover, we assume that the nonlinearity terms f ( t ,...

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Main Author: Abdelhamid Mohammed Djaouti
Format: Article
Language:English
Published: SpringerOpen 2021-01-01
Series:Advances in Difference Equations
Subjects:
Weakly coupled hyperbolic systems
Damped wave equations
Cauchy problem
Global existence
L 2 $L^{2}$ -decay
Effective dissipation
Online Access:https://doi.org/10.1186/s13662-021-03215-0
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spelling doaj-739d3c91c8e4490ca28bbf5ebbeaea9c2021-01-24T12:39:47ZengSpringerOpenAdvances in Difference Equations1687-18472021-01-012021112110.1186/s13662-021-03215-0Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation termsAbdelhamid Mohammed Djaouti0Preparatory Year Deanship, King Faisal UniversityAbstract We prove the global existence of small data solution in all spaces of all dimensions n ≥ 1 $n\geq 1$ for weakly coupled systems of semilinear effectively damped wave, with different time-dependent coefficients in the dissipation terms. Moreover, we assume that the nonlinearity terms f ( t , u ) $f(t,u) $ and g ( t , v ) $g(t,v) $ satisfy some properties of parabolic equations. We study the problem in several classes of regularity.https://doi.org/10.1186/s13662-021-03215-0Weakly coupled hyperbolic systemsDamped wave equationsCauchy problemGlobal existenceL 2 $L^{2}$ -decayEffective dissipation
collection DOAJ
language English
format Article
sources DOAJ
author Abdelhamid Mohammed Djaouti
spellingShingle Abdelhamid Mohammed Djaouti
Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms
Advances in Difference Equations
Weakly coupled hyperbolic systems
Damped wave equations
Cauchy problem
Global existence
L 2 $L^{2}$ -decay
Effective dissipation
author_facet Abdelhamid Mohammed Djaouti
author_sort Abdelhamid Mohammed Djaouti
title Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms
title_short Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms
title_full Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms
title_fullStr Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms
title_full_unstemmed Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms
title_sort modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-01-01
description Abstract We prove the global existence of small data solution in all spaces of all dimensions n ≥ 1 $n\geq 1$ for weakly coupled systems of semilinear effectively damped wave, with different time-dependent coefficients in the dissipation terms. Moreover, we assume that the nonlinearity terms f ( t , u ) $f(t,u) $ and g ( t , v ) $g(t,v) $ satisfy some properties of parabolic equations. We study the problem in several classes of regularity.
topic Weakly coupled hyperbolic systems
Damped wave equations
Cauchy problem
Global existence
L 2 $L^{2}$ -decay
Effective dissipation
url https://doi.org/10.1186/s13662-021-03215-0
work_keys_str_mv AT abdelhamidmohammeddjaouti modifieddifferentnonlinearitiesforweaklycoupledsystemsofsemilineareffectivelydampedwaveswithdifferenttimedependentcoefficientsinthedissipationterms
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