On the loss of regularity for a class of weakly hyperbolic operators

Ebert, Marcelo Rempel; Kapp, R.; Filho, José Ruidival dos Santos

doi:10.1016/j.jmaa.2009.05.026

Journal of Mathematical Analysis and Applications

2009

DOI: 10.1016/j.jmaa.2009.05.026

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On the loss of regularity for a class of weakly hyperbolic operators

Marcelo Rempel Ebert

R. Kapp

José Ruidival dos Santos Filho

Abstract: Keywords:Quasilinear weakly hyperbolic operators Levi conditions Loss of regularity in the Sobolev scale Energy methodIn this paper we determine bounds for the optimal loss of regularity in the Sobolev scale for a class of weakly hyperbolic operators.

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2011

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Existence of solution for the n-dimension second order semilinear hyperbolic equations

Zhang

2011

Journal of Mathematical Analysis and Applications

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In the paper we establish the local and global existence of solution for the n-dimensional second order semilinear hyperbolic equation with a strongly singular coefficient which appears in the boundary-value problems of fluid dynamics. Based on the analysis about the loss of regularity on the line t = 0 for the solution of the corresponding linear equation and the decay at infinity which caused by the singular coefficient, we obtain the existence of a small solution for the semilinear equation by use of fixed point theorem.

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Existence of solution for the n-dimension second order semilinear hyperbolic equations

Zhang

2011

Journal of Mathematical Analysis and Applications

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On the loss of regularity for a class of weakly hyperbolic operators

Abstract: Keywords:Quasilinear weakly hyperbolic operators Levi conditions Loss of regularity in the Sobolev scale Energy methodIn this paper we determine bounds for the optimal loss of regularity in the Sobolev scale for a class of weakly hyperbolic operators.

Cited by 1 publication

References 10 publications

Existence of solution for the n-dimension second order semilinear hyperbolic equations

Existence of solution for the n-dimension second order semilinear hyperbolic equations

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