6533b85efe1ef96bd12c0770

RESEARCH PRODUCT

Radiating and non-radiating sources in elasticity

Yi-hsuan LinEemeli Blåsten

subject

Enclosure010103 numerical & computational mathematicsNavier equation01 natural sciencesinversio-ongelmatTheoretical Computer ScienceMathematics - Analysis of PDEsFOS: Mathematics0101 mathematicsMathematical PhysicsPhysicselastic wavesApplied MathematicsMathematical analysisRegular polygonElasticity (physics)EigenfunctionComputer Science ApplicationsExponential function010101 applied mathematicsInverse source probleminverse source problemsSignal Processingexponential solutions transmission eigenfunctionsFixed frequencyAnalysis of PDEs (math.AP)

description

In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.

yearjournalcountryeditionlanguage
2018-11-20
https://dx.doi.org/10.48550/arxiv.1807.07225