Convergence Rates to Nonlinear Diffusive Waves for Solutions to Nonlinear Hyperbolic System

2019 ◽  
Vol 39 (1) ◽  
pp. 46-56
Author(s):  
Shifeng Geng ◽  
Yanjuan Tang
Keyword(s):  
Hyperbolic System ◽  
Convergence Rates ◽  
Nonlinear Hyperbolic System

Computational Models on Graphs for the Nonlinear Hyperbolic System of Equations

2004 ◽  
Author(s):  
Alexander S. Kholodov ◽  
Yaroslav A. Kholodov
Keyword(s):  
Hyperbolic System ◽  
Human Body ◽  
Partial Derivative ◽  
Computational Models ◽  
Heavy Traffic ◽  
Large River ◽  
System Of Equations ◽  
Information Flows ◽  
Flood Water ◽  
Nonlinear Hyperbolic System

The problems in the form of nonlinear partial derivative equations on graphs (nets, trees) arise in different applications. As the examples of such models we can name the circulatory and respiratory systems of the human body, the model of heavy traffic in the big cities, the model of flood water and pollution propagation in the large river systems, the model of bar structures and frames behavior under the different impacts, the model of the intensive information flows in the computer networks and others.

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.

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