Spatial decay estimates for a class of nonlinear damped hyperbolic equations

F Tahamtani,K Mosaleheh,K Seddighi

doi:10.1155/s0161171201005269

F Tahamtani, K Mosaleheh + Show 1 more

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https://doi.org/10.1155/s0161171201005269

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Abstract

This paper is concerned with investigating the spatial decay estimates for a class of nonlinear damped hyperbolic equations. In addition, we compare the solutions of two‐dimensional wave equations with different damped coefficients and establish an explicit inequality which displays continuous dependence on this coefficient.

Highlights

Spatial decay estimates for several types of partial differential equations and systems have been the subject of extensive investigations in the literature for close to a century and a half
Tahamtani [17] derived an explicit Saint-Venant type decay estimate for solutions of the Dirichlet problem for nonlinear biharmonic equations defined in a semi-infinite cylinder in Rn with homogeneous Dirichlet data on the lateral surface of the cylinder
A spatial decay estimate for transient heat conduction was first given by Edelstein [3]

Summary

Introduction

Spatial decay estimates for several types of partial differential equations and systems have been the subject of extensive investigations in the literature for close to a century and a half. These estimates assert that the solution of the problem decays exponentially with distance from the boundary on which a mechanical or thermal “load” has been applied. Tahamtani [17] derived an explicit Saint-Venant type decay estimate for solutions of the Dirichlet problem for nonlinear biharmonic equations defined in a semi-infinite cylinder in Rn with homogeneous Dirichlet data on the lateral surface of the cylinder.

Results

Conclusion