Abstract formulation of the Cole-Hopf transform
Analysis of PDEs
2019-07-11 v3 Functional Analysis
Exactly Solvable and Integrable Systems
Abstract
Operator representation of Cole-Hopf transform is obtained based on the logarithmic representation of infinitesimal generators. For this purpose the relativistic formulation of abstract evolution equation is introduced. Even independent of the spatial dimension, the Cole-Hopf transform is generalized to a transform between linear and nonlinear equations defined in Banach spaces. In conclusion a role of transform between the evolution operator and its infinitesimal generator is understood in the context of generating nonlinear semigroup.
Keywords
Cite
@article{arxiv.1804.01338,
title = {Abstract formulation of the Cole-Hopf transform},
author = {Yoritaka Iwata},
journal= {arXiv preprint arXiv:1804.01338},
year = {2019}
}
Comments
To be published in Methods of Functional Analysis and Topology; ver.2 (v2) is the accepted version