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Existence of solutions for a nonlinear hyperbolic-parabolic equation in a non-cylinder domain

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  • Marcondes Rodrigues Clark

Abstract

In this paper, we study the existence of global weak solutions for the equation k 2 ( x ) u ″ + k 1 ( x ) u ′ + A ( t ) u + | u | ρ u = f ( I ) in the non-cylinder domain Q in R n + 1 ; k 1 and k 2 are bounded real functions, A ( t ) is the symmetric operator A ( t ) = − ∑ i , j = 1 n ∂ ∂ x j ( a i j ( x , t ) ∂ ∂ x i ) where a i j and f are real functions given in Q . For the proof of existence of global weak solutions we use the Faedo-Galerkin method, compactness arguments and penalization.

Suggested Citation

  • Marcondes Rodrigues Clark, 1996. "Existence of solutions for a nonlinear hyperbolic-parabolic equation in a non-cylinder domain," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:230981
    DOI: 10.1155/S0161171296000221
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