On the discrete heat equation taking values on a tree
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- by Carl Mueller and Kijung Lee PDF
- Proc. Amer. Math. Soc. 137 (2009), 1467-1478 Request permission
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.References
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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
- Received by editor(s): January 9, 2008
- Published electronically: November 18, 2008
- Additional Notes: The first author was supported by NSF and NSA grants
- Communicated by: Richard C. Bradley
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1467-1478
- MSC (2000): Primary 60H15; Secondary 35R60, 35K05
- DOI: https://doi.org/10.1090/S0002-9939-08-09748-7
- MathSciNet review: 2465673