Open Access

# Abstract formulation of the Cole-Hopf transform

### 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.

Key words: Cole-Hopf transform, logarithm of operator, nonlinear semigroup.

### Article Information

 Title Abstract formulation of the Cole-Hopf transform Source Methods Funct. Anal. Topology, Vol. 25 (2019), no. 2, 142-151 MathSciNet MR3978678 Milestones Received 26/04/2018; Revised 03/11/2018 Copyright The Author(s) 2019 (CC BY-SA)

### Authors Information

Yoritaka Iwata
Institute of Innovative Research, Tokyo Institute of Technology; Department of Mathematics, Shibaura Institute of Technology

### Citation Example

Yoritaka Iwata, Abstract formulation of the Cole-Hopf transform, Methods Funct. Anal. Topology 25 (2019), no. 2, 142-151.

### BibTex

@article {MFAT1169,
AUTHOR = {Yoritaka Iwata},
TITLE = {Abstract formulation of the Cole-Hopf transform},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {2},
PAGES = {142-151},
ISSN = {1029-3531},
MRNUMBER = {MR3978678},
URL = {http://mfat.imath.kiev.ua/article/?id=1169},
}

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