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Mathematics > Analysis of PDEs

arXiv:1804.01338 (math)
[Submitted on 4 Apr 2018 (v1), last revised 2 Nov 2018 (this version, v3)]

Title:Abstract formulation of the Cole-Hopf transform

Authors:Yoritaka Iwata
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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.
Comments: To be published in Methods of Functional Analysis and Topology; ver.2 (v2) is the accepted version
Subjects: Analysis of PDEs (math.AP); Functional Analysis (math.FA); Exactly Solvable and Integrable Systems (nlin.SI)
MSC classes: 47D03, 35A20, 34K30
Cite as: arXiv:1804.01338 [math.AP]
  (or arXiv:1804.01338v3 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.01338
Journal reference: Methods Funct. Anal. Topology 25 (2019), no. 2, 142-151

Submission history

From: Yoritaka Iwata [view email]
[v1] Wed, 4 Apr 2018 10:55:09 UTC (10 KB)
[v2] Sun, 22 Jul 2018 07:16:57 UTC (10 KB)
[v3] Fri, 2 Nov 2018 23:56:13 UTC (10 KB)
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