On a Universality of the Heat Equation
โ Scribed by Gerd Herzog
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 121 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
โฆ Synopsis
We prove that there are solutions u ( ~, z ) of the heat equation ut = uxx such that every continuous function f : [a, b] + R can be uniformly approximated by a subsequence of u ( n , . ), n E IN.
๐ SIMILAR VOLUMES
We prove the existence of the Feynman-Kac propagators for the nonautonomous heat equation and the รฐL p ร L q ร-smoothing theorem for the propagators.
Using a new method, we generalize the blow up and existence result from P. Baras and J. A. Goldstein (1984, Trans. Amer. Math. Soc. 284, 121-139) to heat equations on the Heisenberg group. In doing so we need to overcome the difficulty that the equation in this case is both degenerate and of variabl