On the decay in W1,∞ for the 1D semilinear damped wave equation on a bounded domain
- Publication Type
- Original research
- Authors
- Fatima Alzahra Aqel
- Debora Amadori
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.
Journal
- Title
- Discrete & Continuous Dynamical Systems
- Publisher
- American Institute of Mathematical Sciences
- Publisher Country
- United States of America
- Indexing
- Scopus
- Impact Factor
- 1.392
- Publication Type
- Online only
- Volume
- --
- Year
- --
- Pages
- --