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On the discrete heat equation taking values on a tree
Author(s):
Carl
Mueller;
Kijung
Lee
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1467-1478.
MSC (2000):
Primary 60H15;
Secondary 35R60, 35K05
Posted:
November 18, 2008
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Abstract:
This paper was motivated by the question of studying PDE or stochastic PDE taking values on nonsmooth spaces. This is a hard problem in general, so we concentrate on a test case: the heat equation taking values on the union of rays emanating from the origin. We construct a series of discrete approximation to the solution and show that they converge to a limit. Unfortunately, we do not know if the limit is uniqueness. Our tools are probabilistic, exploiting the well-known connection between Brownian motion and the heat equation.
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Additional Information:
Carl
Mueller
Affiliation:
Department of Mathematics, University of Rochester, Rochester, New York 14627
Email:
cmlr@math.rochester.edu
Kijung
Lee
Affiliation:
Department of Mathematics, Yonsei University, Seoul 120-749, Republic of Korea
Email:
kijung@yonsei.ac.kr
DOI:
10.1090/S0002-9939-08-09748-7
PII:
S 0002-9939(08)09748-7
Keywords:
Heat equation,
white noise,
stochastic partial differential equations
Received by editor(s):
January 9, 2008
Posted:
November 18, 2008
Additional Notes:
The first author was supported by NSF and NSA grants
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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