Decay of solutions of a nonlinear hyperbolic system in noncylindrical domain

Tania Nunes Rabello

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-10

Abstract:

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 Q u = 0 on Σ u ( 0 ) = u ο u 1 ( 0 ) = u 1 where Q is a noncylindrical domain of ℝ n + 1 with lateral boundary Σ , u − ( u 1 , u 2 ) a vector defined on Q , { A ( t ) , 0 ≤ t ≤ + ∞ } is a family of operators in ℒ ( H ο 1 ( Ω ) , H − 1 ( Ω ) ) , where A ( t ) u = ( A ( t ) u 1 , A ( t ) u 2 ) and G : ℝ 2 → ℝ 2 a continuous function such that x . G ( x ) ≥ 0 , for x ∈ ℝ 2 .

Moreover, we obtain that the solutions of the above system with dissipative term u ′ have exponential decay.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:425794

DOI: 10.1155/S0161171294000815

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