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Green's functions for elliptic and parabolic equations with random coefficients II
Author(s):
Joseph
G.
Conlon
Journal:
Trans. Amer. Math. Soc.
356
(2004),
4085-4142.
MSC (2000):
Primary 81T08, 82B20, 35R60, 60J75
Posted:
January 16, 2004
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Abstract:
This paper is concerned with linear parabolic partial differential equations in divergence form and their discrete analogues. It is assumed that the coefficients of the equation are stationary random variables, random in both space and time. The Green's functions for the equations are then random variables. Regularity properties for expectation values of Green's functions are obtained. In particular, it is shown that the expectation value is a continuously differentiable function in the space variable whose derivatives are bounded by the corresponding derivatives of the Green's function for the heat equation. Similar results are obtained for the related finite difference equations. This paper generalises results of a previous paper which considered the case when the coefficients are constant in time but random in space.
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Additional Information:
Joseph
G.
Conlon
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Email:
conlon@umich.edu
DOI:
10.1090/S0002-9947-04-03467-1
PII:
S 0002-9947(04)03467-1
Keywords:
pde with random coefficients,
homogenization
Received by editor(s):
July 23, 2002
Received by editor(s) in revised form:
July 15, 2003
Posted:
January 16, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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