On a nonlinear degenerate evolution equation with strong damping

Jorge Ferreira and Ducival Carvalho Pereira

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-10

Abstract:

In this paper we consider the nonlinear degenerate evolution equation with strong damping, ( * ) { K ( x , t ) u t t − Δ u − Δ u t + F ( u ) = 0 in Q = Ω × ] 0 , T [ u ( x , 0 ) = u 0 , ( k u ′ ) ( x , 0 ) = 0 in Ω u ( x , t ) = 0 on ∑ = Γ × ] 0 , T [ where K is a function with K ( x , t ) ≥ 0 , K ( x , 0 ) = 0 and F is a continuous real function satisfying ( * * ) s F ( s ) ≥ 0 , for all s ∈ R , Ω is a bounded domain of R n , with smooth boundary Γ . We prove the existence of a global weak solution for (*).

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:603689

DOI: 10.1155/S016117129200070X

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