Well-posedness and Energy Decay of Solutions to a Nonlinear Bresse System with Delay Terms

被引：0
|
作者：
Benaissa, Abbes [1 ]
Miloudi, Mostefa [1 ]
Mokhtari, Mokhtar [1 ]
机构：
[1] Univ Djillali Liabes Sidi Bel Abbes, Lab Anal & Control Partial Differential Equat, POB 89, Sidi Bel Abbes 22000, Algeria
来源：
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2020年 / 28卷 / 02期
关键词：
Nonlinear Bresse system; Delay terms; Faedo-Galerkin method; Decay rate; Multiplier method; TIMOSHENKO SYSTEM; WAVE-EQUATION; BOUNDARY; STABILIZATION; STABILITY; RATES;
D O I：
10.1007/s12591-016-0339-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Bresse system in bounded domain with delay terms in the nonlinear internal feedbacks {rho(1)phi(tt)-Gh(phi(x)+psi+l omega)x-lEh(omega(x)-l phi)+mu(1)g(1)(phi(t)(x,t))+mu(2)g(2)(phi(t)(x,t-tau(1)))=0 rho(2)psi(tt)-EI psi(xx)+Gh(phi(x)+psi+l omega)+(mu(1)) over tilde(g(1)) over tilde(psi(t)(x,t))+(mu(2)) over tilde(g(2)) over tilde(psi(t)(x,t-tau(2)))=0 rho(1)omega(tt)-Eh(omega(x)-l(phi))(x)+lGh(phi(x)+psi+l omega)+(sic)u(1) (sic)g(1)(omega(t)(x,t))+(sic)mu(2)(sic)(g2)(omega t(x,t-tau(3)))=0 and prove the global existence of its solutions in Sobolev spaces by means by means of the energy method combined with the Faedo-Galerkin procedure under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method and some weighted integral inequalities.
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收藏
页码：447 / 478
页数：32
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