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

TL;DR

This paper proves the unique solvability of a time-harmonic elasticity problem in a half-strip with mixed boundary conditions, using a solution form combining outgoing waves and exponentially decreasing functions.

Contribution

It establishes well-posedness of the elasticity problem in a half-strip with specific boundary conditions, under a novel solution framework.

Findings

Unique weak solution exists under specified conditions.

Solution form includes outgoing waves and exponential decay.

Results contribute to mathematical elasticity theory.

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).