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Feynman formulae for a parabolic equation with biharmonic differential operator on a configuration space
Engineering Education # 08, August 2012
DOI: 10.7463/0812.0445534
The Cauchy problem for a parabolic partial differential equation with biharmonic operator and additive perturbation is considered in this note. Such equations are used in different  domains of physics, chemistry, biology, and computer sciences.  The solution of the considered problem is represented by Feynman formulae, i.e. by limits of iterated integrals of elementary functions when multiplicity if integrals tends to infinity.  The main part of these formulae is proved  with the help of Chernoff's theorem; some formulae are obtained on the base of the Yosida approximations.  Different types of Feynman formulae are presented in this work: Lagrangin and Hamiltonian. Lagrangian Feynman formulae are suitable for computer modeling of the considered dynamics. Hamiltonian Feynman formulae are related to some phase space Feynman path integrals; such integrals are important objects in quantum physics.
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