The Feynman approximation for the solution of heat equation on branching manifolds   28 October 2013


Viktoryia Dubravina, University of Russia

We shall investigate the Feynman approximation for the solutions of Cauchy problem for special type of differentional equations of second order of a branching manifold Y3. These solutions will be represented as a limit of multiple integrals over Cartesian powers of configuration space, as multiplicity tends to infinity. Such representations are called a Lagrangian Feynman formulae. We consider the collection of differentional equations which can describe the diffusion or similar processes on a branching manifold Y3, which can be described as a Cartesian multiplication of a real line R and a graph consisting of one vertex and 3 rays. The coefficients of heat conductivity are considered to be the parameters of our equations. And their solutions satisfy natural border conditions - the consistence of functions on common line of Y3 and the analogue of Kirchhoff’s circuit law (the sum of derivatives of the solution taken with coefficients, equals 0). These conditions specify the Feynman formula which is used to solve the problem.

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Viktoryia Dubravina University of Russia 28/10/2013 - 28/10/2013
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