On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms
We prove existence and uniform stability of strong solutions to a quasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity of the type u″−M(∫Ω|∇u|2dx)Δu+a(x)g(u′)+f(u)=0, in Ω×]0,+∞[, u=0, on Γ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), in Ω....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2005-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/JAM.2005.219 |
| Summary: | We prove existence and uniform stability of strong solutions to a
quasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity of
the type u″−M(∫Ω|∇u|2dx)Δu+a(x)g(u′)+f(u)=0, in Ω×]0,+∞[, u=0, on Γ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), in Ω. |
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| ISSN: | 1110-757X 1687-0042 |