Nondivergence form quasilinear heat equations driven by space-time white noise
M\'at\'e Gerencs\'er
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.
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 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.
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11institutetext: IST Austria
Nondivergence form quasilinear heat equations driven by space-time white noise
Máté Gerencsér
Abstract
We give a Wong-Zakai type characterisation of the solutions of quasilinear heat equations driven by space-time white noise in 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.
Contents
1 Introduction
The main goal of the present paper is to ‘solve’ the equation
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