Cauchy problem for an essentially infinite-dimensional parabolic equation with variable coefficients

1994 ◽  
Vol 46 (6) ◽  
pp. 714-724
Author(s):  
Yu. V. Bogdanskii
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Variable Coefficients ◽  
Infinite Dimensional

Regularization of a non-characteristic Cauchy problem for a parabolic equation

1995 ◽  
Vol 11 (6) ◽  
pp. 1247-1263 ◽  
Author(s):  
Dinh Nho Hao ◽  
A Schneiders ◽  
H -J Reinhardt
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Characteristic Cauchy Problem

FEYNMAN FORMULAS FOR AN INFINITE-DIMENSIONAL 𝔭-ADIC HEAT TYPE EQUATION

2011 ◽  
Vol 14 (01) ◽  
pp. 137-148 ◽  
Author(s):  
OLGA BELOSHAPKA
Keyword(s):  
Cauchy Problem ◽  
Configuration Space ◽  
Short Note ◽  
Type Equation ◽  
Spatial Variable ◽  
Feynman Formula ◽  
Cartesian Products ◽  
Infinite Dimensional

Smolyanov has introduced1 the term "Feynman formula" (in the configuration space) for the representation of a solution of a Cauchy problem by limit of integrals over finite Cartesian products of the domain of the solution when the number of multipliers tends to infinity. In this paper, such formulas (first written by Smolyanov, Shamarov and Kpekpassi in a short note2) are proved for a family of heat type equations where the spatial variable runs over 𝔭-adic space of countable sequences. Equations with 𝔭-adic variables describe, for example, the dynamics of proteins.

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