Well-posedness of a time-harmonic elasticity problem in a half-strip

2022/06/22 by Akian, Jean-Luc
#46E35 #47A53 #74B05 #74H20 #74H25 #74J05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2206.11012

Abstract

In this paper we establish that the time-harmonic elasticity problem in a half-strip with non-homogeneous Dirichlet conditions on its boundary section and traction-free conditions on its upper and lower boundaries, has a unique weak solution when this solution is searched under the form of the sum of a linear combination of outgoing waves and an exponentialy decreasing function (in the sense of weighted Sobolev spaces).

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