Abstract formulation of the Cole-Hopf transform

Authors

  • Y. Iwata Institute of Innovative Research, Tokyo Institute of Technology; Department of Mathematics, Shibaura Institute of Technology

DOI:

Keywords:

Cole-Hopf transform, logarithm of operator, nonlinear semigroup

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.

Downloads

Published

2019-06-25

Issue

Vol. 25 No. 2 (2019)

Section

Articles

How to Cite

Iwata, Y. “Abstract Formulation of the Cole-Hopf Transform”. Methods of Functional Analysis and Topology, vol. 25, no. 2, June 2019, pp. 142-51, https://zen.imath.kiev.ua/index.php/mfat/article/view/718.