Radiating and non-radiating sources in elasticity

Abstract

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.

arXiv comment17 pages

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Cited by in corpus (14)

• On an electromagnetic problem in a corner and its applications
• On a local geometric property of the generalized elastic transmission eigenfunctions and application
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• Extracting discontinuity using the probe and enclosure methods
• Fast inverse elastic scattering of multiple particles in three dimensions
• Factorization method for inverse time-harmonic elastic scattering with a single plane wave
• A New Type of CGO Solutions and its Applications in Corner Scattering
• Local geometric properties of conductive transmission eigenfunctions and applications
• On local and global structures of transmission eigenfunctions and beyond
• Geometrical and topological properties of transmission resonance and artificial mirage
• On new surface-localized transmission eigenmodes
• On generalized Holmgren's principle to the Lamé operator with applications to inverse elastic problems
• Cones with convoluted geometry that always scatter or radiate
• Surface-localized transmission eigenstates, super-resolution imaging and pseudo surface plasmon modes