# American Institute of Mathematical Sciences

July  2015, 14(4): 1469-1480. doi: 10.3934/cpaa.2015.14.1469

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

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

Received  September 2013 Revised  December 2013 Published  April 2015

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.
Citation: Hideo Kubo. On the pointwise decay estimate for the wave equation with compactly supported forcing term. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1469-1480. doi: 10.3934/cpaa.2015.14.1469
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