Anisotropic diffusions with singular advections and absorptions part 1: existence

Existence, Uniqueness and the Strong Markov Property of Solutions to Kimura Diffusions with Singular Drift

Motivated by applications to proving regularity of solutions to degenerate parabolic equations arising in population genetics, we study existence, uniqueness and the strong Markov property of weak solutions to a class of degenerate stochastic differential equations. The stochastic differential equations considered in our article admit solutions supported in the set [0,∞)×R, and they are degener...

Some Anisotropic Diffusions

Since the seminal works of Mumford-Shah [16] and Perona-Malik [18], variational and PDE-based methods have found a wide range of applications in Image Processing and have generated steady interest in the mathematical community. The latter is at least partly due to the difficulties one encounters in developing a mathematical theory encopassing equations which are often ill-posed albeit practical...

Class of Limit Theorems for Singular Diffusions

Mean Field Limit for Disordered Diffusions with Singular Interactions

Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in R in the presence of a random environment and with spatial extension: each diffusion is attached to one site of the lattice Z, and the interaction between two diffusions is attenuated by a spatial weight that depends on ...

Anisotropic viscoelastic models with singular memory

The physical background of singular memory models and in particular the Cole–Cole model is discussed. Three models of anisotropic linear viscoelasticity with frequency-dependent stiffness coefficients are considered. The models are constructed in such a way that anisotropic properties are separated from anelastic effects. Two of these models represent finite-speed wave propagation with singular...