Year: 2025
Type: article
Abstract: . This paper focuses on an elastic dislocation problem that is motivated by applications in the geophysical and seismological communities. In our model, the displacement satisfies the Lamé system in a bounded domain with a mixed homogeneous boundary condition. We also allow the occurrence of discontinuities in both the displacement and traction fields on the fault curve/surface. By the variational approach, we first prove the well-posedness of the direct dislocation problem in a rather general setting with the Lamé parameters being real-valued [Formula: see text] functions and satisfy the strong convexity condition. Next, by considering that the Lamé parameters are constant and the fault curve/surface possesses certain corner singularities, we establish a local characterization of the jump vectors at the corner points over the dislocation curve/surface. In our study, the dislocation is geometrically rather general and may be open or closed. We establish the unique results for the inverse problem of determining the dislocation curve/surface and the jump vectors for both cases.
DOI: 10.1137/24m1710267
Authors: Huaian Diao, Hongyu Liu, Qingle Meng
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: Mathematical study of fields concentration and gradient estimates with applications, G3549053223, New development on pattern formations of coupled PDEs with transparent boundary conditions and applications, Mathematical studies of surface-localized transmission eigenstates and applications, Geometric properties of three classes of spectral problems with applications to inverse problems and material sciences, G8653774208
OpenAlex ID: W4415302316