The Green’s functions for peridynamic non-local diffusion

Peridynamic thermal diffusion

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Greens Functions for the Wave Equation

I gather together known results on fundamental solutions to the wave equation in free space, and Greens functions in tori, boxes, and other domains. From this the corresponding fundamental solutions for the Helmholtz equation are derived, and, for the 2D case the semiclassical approximation interpreted back in the time-domain. Utility: scarring via time-dependent propagation in cavities; Math 4...

Greens Functions for 3-D Seismic Migration

The space-time Greens functions for 3-D poststack and 3-D prestack migration in a homogeneous medium are derived under the fareld approximation. These Greens functions can be used to practically compute synthetic migrated images. Examples are given for the recording footprint noise associated with a point scatterer and a meandering river channel. The Greens functions also provide fundamental in...

Non-local Diffusion

Boundary Fluxes for Non-local Diffusion

Abstract. We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we l...