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

## TL;DR

This paper characterizes solutions to one-dimensional quasilinear heat equations driven by space-time white noise, using a Wong-Zakai type approach and a novel integration by parts formula to handle renormalization.

## Contribution

It introduces a new method for analyzing quasilinear SPDEs driven by space-time white noise, including a detailed renormalization scheme and a general integration by parts formula.

## Key findings

- Renormalization counterterms are shown to be local in the solution.
- A comprehensive arrangement of hundreds of terms ensures correct renormalization.
- A new integration by parts formula provides identities for renormalization constants.

## 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.