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Renormalized-generalized solutions for the KPZ equation

Pedro Catuogno

Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970 – Campinas – SP, Brazil

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and

Christian Olivera

Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970 – Campinas – SP, Brazil

Corresponding author.

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https://doi.org/10.1142/S0219025714500271Cited by:0 (Source: Crossref)

Abstract

This work introduces a new notion of solution for the KPZ equation, in particular, our approach encompasses the Cole–Hopf solution. We set in the context of the distribution theory the proposed results by Bertini and Giacomin from the mid '90s.

This new approach provides a pathwise notion of solution as well as a structured approximation theory. The developments are based on regularization arguments from the theory of distributions.

Keywords:

AMSC: 46F99, 46F30, 60H15

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