69 citations · 242 across the 49 of their papers we have counts for
4 papers · 1 filter
Semi-discretization for stochastic scalar conservation laws with multiple rough fluxes
Benjamin Gess, Benoît Perthame, Panagiotis E. Souganidis
We develop a semi-discretization approximation for scalar conservation laws with multiple rough time dependence in inhomogeneous fluxes. The method is based on Brenier's transport-…
Free boundary problems for Tumor Growth: a Viscosity solutions approach
Inwon C. Kim, Benoit Perthame, Panagiotis E. Souganidis
The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free bou…
Rare mutations limit of a steady state dispersion trait model
Benoit Perthame, Panagiotis E. Souganidis
The evolution of dispersal is a classical question in evolutionary ecology, which has been widely studied with several mathematical models. The main question is to define the fitte…
Metastability for parabolic equations with drift: part II. The quasilinear case
Hitoshi Ishii, Panagiotis E. Souganidis
This is the second part of our series of papers on metastability results for parabolic equations with drift. The aim is to present a self-contained study, using partial differentia…