On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms

E. Cabanillas Lapa, Z. Huaringa Segura and F. Leon Barboza

Journal of Applied Mathematics, 2005, vol. 2005, 1-15

Abstract:

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 | 2 d x ) Δ u + a ( x ) g ( u ′ ) + f ( u ) = 0 , in Ω × ] 0 , + ∞ [ , u = 0 , on Γ × ] 0 , + ∞ [ , u ( x , 0 ) = u 0 ( x ) , u ′ ( x , 0 ) = u 1 ( x ) , in Ω .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:975040

DOI: 10.1155/JAM.2005.219

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