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math-ph2024
The Steklov problem for exterior domains: asymptotic behavior and applications
Denis S. Grebenkov, Adrien Chaigneau
We investigate the spectral properties of the Steklov problem for the modified Helmholtz equation in the exterior of a compact set, for which the positive parameter $…
math-ph2024
Spectral properties of the Dirichlet-to-Neumann operator for spheroids
Denis S. Grebenkov
We study the spectral properties of the Dirichlet-to-Neumann operator and the related Steklov problem in spheroidal domains ranging from a needle to a disk. An explicit matrix repr…
math-ph2023
Spectral properties of the Bloch-Torrey operator in three dimensions
Denis S. Grebenkov
We consider the Bloch-Torrey operator, , that governs the time evolution of the transverse magnetization in diffusion magnetic resonance imaging (dMRI). Using the matrix f…