On the existence of solutions of strongly damped nonlinear wave equations

Jong Yeoul Park and Jeong Ja Bae

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-14

Abstract:

We investigate the existence and uniqueness of solutions of the following equation of hyperbolic type with a strong dissipation: u t t ( t , x ) − ( α + β ( ∫ Ω | ∇ u ( t , y ) | 2 d y ) γ ) Δ u ( t , x )                                                                 − λ Δ u t ( t , x ) + μ | u ( t , x ) | q − 1 u ( t , x ) = 0 ,           x ∈ Ω , t ≥ 0                         u ( 0 , x ) = u 0 ( x ) ,                     u t ( 0 , x ) = u 1 ( x ) ,             x ∈ Ω ,     u | ∂ Ω = 0 , where q > 1 , λ > 0 , μ ∈ ℠, α , β ≥ 0 , α + β > 0 , and Δ is the Laplacian in ℠N .

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:273142

DOI: 10.1155/S0161171200000971

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