UNSPECIFIED (1994) APPROXIMATE TRAVELING WAVES FOR GENERALIZED KPP EQUATIONS AND CLASSICAL MECHANICS. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 446 (1928). pp. 529-554. ISSN 1364-5021

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Abstract

We consider the existence of approximate travelling waves of generalized KPP equations in which the initial distribution can depend on a small parameter mu which in the limit mu --> 0 is the sum of some delta-functions or a step function. Using the method of Elworthy & Truman (1982) we construct a classical path which is the backward flow of a classical newtonian mechanics with given initial position and velocity before the time at which the caustic appears. By the Feynman-Kac formula and the Maruyama-Girsanov-Cameron-Martin transformation we obtain an identity from which, with a late caustic assumption, we see the propagation of the global wave front and the shape of the trough. Our theory shows clearly how the initial distribution contributes to the propagation of the travelling wave. Finally, we prove a Huygens principle for KPP equations on complete riemannian manifolds without cut locus, with some bounds on their volume element, in particular Cartan-Hadamard manifolds.

Item Type:	Journal Article
Subjects:	Q Science
Journal or Publication Title:	PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Publisher:	ROYAL SOC LONDON
ISSN:	1364-5021
Date:	8 September 1994
Volume:	446
Number:	1928
Number of Pages:	26
Page Range:	pp. 529-554
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/20330

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