Singular initial conditions for the heat equation with a noise term
In: Annals of probability, Jg. 24 (1996), Heft 1, S. 377-398
Online
academicJournal
- print, 6 ref
Zugriff:
We consider the equation ut = uxx + uγW, t > 0,0 ≤ x ≤ J, u(0,x) = u0(x), u(t,0) = u(t,J) = 0, where W = W(t,x) is two-parameter white noise. We show local existence and uniqueness for unbounded initial conditions satisfying certain conditions. Our results are motivated by earlier work, which showed that, for large y, solutions of this equation can blow up. One would wish to show that solutions can be extended beyond blowup, and our results can be viewed as a step in that direction.
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Singular initial conditions for the heat equation with a noise term
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Autor/in / Beteiligte Person: | MUELLER, C |
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Zeitschrift: | Annals of probability, Jg. 24 (1996), Heft 1, S. 377-398 |
Veröffentlichung: | Hayward, CA: Institute of Mathematical Statistics, 1996 |
Medientyp: | academicJournal |
Umfang: | print, 6 ref |
ISSN: | 0091-1798 (print) |
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