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Propagation of chaos and the Hopf-Cole transformation. (English) Zbl 0606.35041
In a previous paper it has been shown that Burgers’ equation constitutes a limit of a contracted N-body problem when N tends to infinity. By proving that the L-operator may be transformed into a Laplacian \(\Delta\), by using an intertwining operator Q, an unsuccesful attempt was made to obtain a linearizing transformation for the Burgers equation in order to achieve a Hopf-Cole transformation.
In this paper the difficulties encountered previously were by-passed and a transformation closely related to the Hopf-Cole transformation was established. The transformation may be used to define the nonlinear evolution equations, which can be obtained by contraction from N-body linear problems, and distinguish the nonlinear equations which can be linearized by using the approximate approach established in this paper.
Reviewer: P.Theocaris

MSC:
35K55 Nonlinear parabolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
35Q99 Partial differential equations of mathematical physics and other areas of application
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References:
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