In this paper we study a 2×2 semilinear hyperbolic system of partial differential equations, which is related to a semilinear wave equation with nonlinear, time-dependent damping in one space dimension. For this problem, we prove a well-posedness result in L∞L∞ in the space-time domain (0,1)×[0,+∞). Then we address the problem of the time-asymptotic stability of the zero solution and show that, under appropriate conditions, the solution decays to zero at an exponential rate in the space L∞. The proofs are based on the analysis of the invariant domain of the unknowns, for which we show a contractive property. These results can yield a decay property in W^{1,∞} for the corresponding solution to the semilinear wave equation.

العنوان

Discrete & Continuous Dynamical Systems

الناشر

American Institute of Mathematical Sciences

بلد الناشر

الولايات المتحدة الأمريكية

Indexing

Scopus

معامل التأثير

1,392

نوع المنشور

إلكتروني فقط

المجلد

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السنة

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الصفحات

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