BURGERS EQUATION AND KOLMOGOROV–PETROVSKY–PISKUNOV EQUATION ON MANIFOLDS-Reference-Cited by-同舟云学术

BURGERS EQUATION AND KOLMOGOROV–PETROVSKY–PISKUNOV EQUATION ON MANIFOLDS

Published:2011-06 Issue:02 Volume:14 Page:199-208
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

MATSKEVICH S. E.¹

Affiliation:

1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia

Abstract

In this paper the analogue of the Hopf–Cole transformation is introduced for manifolds. It has been shown that under certain conditions this transformation connects the Burgers equation and Kolmogorov–Petrovsky–Piskunov equation on pseudo-Riemannian manifolds.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025711004341

Reference16 articles.

1. G. Arfken, Mathematical Methods for Physicists, 3rd edn. (Academic Press, 1985) p. 165.

2. Generalized Solutions of Nonlinear Parabolic Systems and the Vanishing Viscosity Method

3. The stochastic Burgers Equation

4. Stochastic heat and Burgers equations and their singularities. I. Geometrical properties

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