Geodesic
Nondivergence form quasilinear heat equations driven by space-time white noise
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 663-682

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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.

DOI : 10.1016/j.anihpc.2020.01.003
Classification : 60H15, 60L30
Keywords: Stochastic partial differential equations, Renormalisation, Regularity structures, Quasilinear equations 
@article{AIHPC_2020__37_3_663_0,
     author = {Gerencs\'er, M\'at\'e},
     title = {Nondivergence form quasilinear heat equations driven by space-time white noise},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {663--682},
     publisher = {Elsevier},
     volume = {37},
     number = {3},
     year = {2020},
     doi = {10.1016/j.anihpc.2020.01.003},
     mrnumber = {4093623},
     zbl = {1446.60051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.01.003/}
}
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Gerencsér, Máté. Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 663-682. doi: 10.1016/j.anihpc.2020.01.003

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