Geodesic
Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 189-206

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution. 
@article{BUMI_2004_8_7B_1_a7,
     author = {Secchi, Paolo},
     title = {Pointwise decay for solutions of the {2D} {Neumann} exterior problem for the wave equation},
     journal = {Bollettino della Unione matematica italiana},
     pages = {189--206},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
     number = {1},
     year = {2004},
     zbl = {1178.35231},
     mrnumber = {MR2044266},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a7/}
}
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Secchi, Paolo. Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 189-206. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a7/