Pathwise Well-Posedness of the Fast Diffusion Equation with Affine Multiplicative Noise

Ben Fehrman (MPI-MIS Leipzig)

In this talk, which describes joint work with Benjamin Gess, I will discuss the existence and uniqueness of pathwise entropy solutions for the fast diffusion equation driven by affine multiplicative noise.  The theory of such solutions is motivated by the study of stochastic viscosity solutions, and was first developed in the context of scalar conservation laws with rough fluxes by Lions, Perthame and Souganidis, and later extended by Gess and Souganidis.  Their approach is based upon the kinetic formulation of the equation, and involves testing the solution against data propagating along the corresponding path-dependent characteristics.  I hope to describe the analogous theory in the context of the fast-diffusion equation, and to explain how it can be used to establish the well-posedness of pathwise entropy solutions in this setting.

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