On the pointwise decay estimate for the wave equationwith compactly supported forcing term

Hideo Kubo

doi:10.3934/cpaa.2015.14.1469

Article Contents

2015, Volume 14, Issue 4: 1469-1480. Doi: 10.3934/cpaa.2015.14.1469

This issue Previous Article A numerical approach to Blow-up issues for Davey-Stewartson II systems Next Article A sharp scattering condition for focusing mass-subcritical nonlinear Schrödinger equation

On the pointwise decay estimate for the wave equation with compactly supported forcing term

Hideo Kubo^1,

1.
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810

Received: September 2013

Revised: December 2013

Published: July 2015

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Abstract

In this paper we derive a new type of pointwise decay estimates for solutions to the Cauchy problem for the wave equation in 2D, in the sense that one can diminish the weight in the time variable for the forcing term if it is compactly supported in the spatial variables. As an application of the estimate, we also establish an improved decay estimate for the solution to the exterior problem in 2D.

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Mathematics Subject Classification: Primary: 35L15; Secondary: 35L20.

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References

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