Geodesic
Energy decay in a wave guide with dissipation at infinity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 519-549

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We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a positive constant, and we obtain the diffusive phenomenon typical for the contribution of low frequencies when the damping is effective at infinity. On the other hand, the usual Geometric Control Condition is not necessarily satisfied so we may have a loss of regularity for the contribution of high frequencies. Since our results are new even in the Euclidean space, we also state a similar result in this case.

DOI : 10.1051/cocv/2017054
Classification : 35L05, 35J10, 35J25, 35B40, 47A10, 47B44
Keywords: Local and global energy decay, dissipative wave equation, wave guides, diffusive phenomenon, semiclassical analysis, low frequency resolvent estimates

Malloug, Mohamed 1 ; Royer, Julien 1

1 
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     title = {Energy decay in a wave guide with dissipation at infinity},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {519--549},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {2},
     year = {2018},
     doi = {10.1051/cocv/2017054},
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     zbl = {1409.35032},
     language = {en},
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Malloug, Mohamed; Royer, Julien. Energy decay in a wave guide with dissipation at infinity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 519-549. doi: 10.1051/cocv/2017054

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