Long-time existence for signed solutions of the heat equation with a noise term |
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Authors: | Carl Mueller |
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Institution: | (1) Deptartment of Mathematics, University of Rochester, Rochester, NY 14627, USA (cmlr@troi.cc.rochester.edu), US |
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Abstract: | Summary. Let ? be the circle 0,J] with the ends identified. We prove long-time existence for the following equation.
Here, =(t,x) is 2-parameter white noise, and we assume that u
0(x) is a continuous function on ?. We show that if g(u) grows no faster than C
0(1+|u|)γ for some γ<3/2, C
0>0, then this equation has a unique solution u(t,x) valid for all times t>0.
Received: 27 November 1996 / In revised form: 28 July 1997 |
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Keywords: | AMS Mathematics Subject Classification (1991): Primary 60H15 secondary 35R60 |
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