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Exponential boundary stabilization for nonlinear wave equations with localized damping and nonlinear boundary condition
- Source :
- Communications on Pure & Applied Analysis. 16:1571-1585
- Publication Year :
- 2017
- Publisher :
- American Institute of Mathematical Sciences (AIMS), 2017.
-
Abstract
- Let \begin{document}$ D\subset R^{d}$\end{document} be a bounded domain in the \begin{document}$d- $\end{document} dimensional Euclidian space \begin{document}$R^{d} $\end{document} with smooth boundary $Γ=\partial D.$ In this paper we consider exponential boundary stabilization for weak solutions to the wave equation with nonlinear boundary condition: \begin{document}$\left\{ \begin{gathered}u_{tt}(t)-ρ(t)Δ u(t)+b(x)u_{t}(t)=f(u(t)), \\ u(t)=0\ \ \text{on }Γ_{0}×(0,T), \\ \dfrac{\partial u(t)}{\partialν}+γ(u_{t}(t))=0\ \ \text{on }Γ _{1}×(0,T), \\ u(0)=u_{0},u_{t}(0)=u_{1},\end{gathered} \right.$ \end{document} where \begin{document}$\left\| {{u_0}} \right\| \begin{document}$ E(0) where \begin{document}$λ_{β}, $\end{document} \begin{document}$d_{β} $\end{document} are defined in (21), (22) and \begin{document}$Γ=Γ_{0}\cupΓ_{1} $\end{document} and \begin{document}$\bar{Γ}_{0}\cap\bar{Γ}_{1}=φ. $\end{document}
- Subjects :
- Physics
Applied Mathematics
010102 general mathematics
Mathematical analysis
Boundary (topology)
General Medicine
01 natural sciences
Nonlinear boundary conditions
Exponential function
010101 applied mathematics
Combinatorics
Nonlinear wave equation
Domain (ring theory)
0101 mathematics
Analysis
Subjects
Details
- ISSN :
- 15535258
- Volume :
- 16
- Database :
- OpenAIRE
- Journal :
- Communications on Pure & Applied Analysis
- Accession number :
- edsair.doi...........900a64c62feda82f5178e29ae2fb4c1c