scholarly journals Decay of solutions of a nonlinear hyperbolic system in noncylindrical domain

1994 ◽  
Vol 17 (3) ◽  
pp. 561-570 ◽  
Author(s):  
Tania Nunes Rabello
Keyword(s):  
Continuous Function ◽  
Hyperbolic System ◽  
Exponential Decay ◽  
Existence Of Solutions ◽  
Lateral Boundary ◽  
Dissipative Term ◽  
Noncylindrical Domain ◽  
Nonlinear Hyperbolic System ◽  
Decay Of Solutions

In this paper we study the existence of solutions of the following nonlinear hyperbolic svstem|u″+A(t)u+b(x)G(u)=f   in   Qu=0   on   Σu(0)=uο   u1(0)=u1whereQis a noncylindrical domain ofℝn+1with lateral boundaryΣ,u−(u1,u2)a vector defined onQ,{A(t),   0≤t≤+∞}is a family of operators inℒ(Hο1(Ω),H−1(Ω)), whereA(t)u=(A(t)u1,A(t)u2)andG:ℝ2→ℝ2a continuous function such thatx.G(x)≥0, forx∈ℝ2.Moreover, we obtain that the solutions of the above system with dissipative termu′have exponential decay.

THE ZERO DIFFUSION LIMIT FOR NONLINEAR HYPERBOLIC SYSTEM WITH DAMPING AND DIFFUSION

2008 ◽  
Vol 05 (04) ◽  
pp. 767-783 ◽  
Author(s):  
KAIMAO CHEN ◽  
CHANGJIANG ZHU
Keyword(s):  
Hyperbolic System ◽  
Existence Of Solutions ◽  
Diffusion Limit ◽  
Linear Diffusion ◽  
Diffusion Waves ◽  
Global Existence Of Solutions ◽  
Nonlinear Hyperbolic System ◽  
The Cauchy Problem ◽  
Zero Diffusion Limit ◽  
And Diffusion

We consider the Cauchy problem for a nonlinear hyperbolic system with damping and diffusion. Thanks to a suitably constructed corrector function, we can eliminate the layer at infinity and by using the energy method we establish the global existence of solutions if the initial data is a small perturbation around the corresponding linear diffusion waves. Furthermore, we study the zero diffusion limit and, precisely, we show that the sequence of solutions converges to the corresponding hyperbolic system as the diffusion parameter tends to zero.

scholarly journals On the System of Coupled Nondegenerate Kirchhoff Equations with Distributed Delay: Global Existence and Exponential Decay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Salem Alkhalaf ◽  
Ibrahim Mekawy ◽  
...  
Keyword(s):  
Global Existence ◽  
Exponential Stability ◽  
Galerkin Method ◽  
Exponential Decay ◽  
Energy Method ◽  
Existence Of Solutions ◽  
Distributed Delay ◽  
Stability Result ◽  
Kirchhoff Equations ◽  
Global Existence Of Solutions

This paper studies the system of coupled nondegenerate viscoelastic Kirchhoff equations with a distributed delay. By using the energy method and Faedo-Galerkin method, we prove the global existence of solutions. Furthermore, we prove the exponential stability result.

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