Nondivergence form quasilinear heat equations driven by space-time white noise

Máté Gerencsér

doi:10.1016/j.anihpc.2020.01.003

paper

Nondivergence form quasilinear heat equations driven by space-time white noise

arXiv:1902.07635 · doi:10.1016/j.anihpc.2020.01.003

Abstract

We give a Wong-Zakai type characterisation of the solutions of quasilinear heat equations driven by space-time white noise in $1 + 1$ dimensions. In order to show that the renormalisation counterterms are local in the solution, a careful arrangement of a few hundred terms is required. The main tool in this computation is a general integration by parts formula that provides a number of linear identities for the renormalisation constants.

23 pages