Singular initial conditions for the heat equation with a noise term
Mueller, Carl
Ann. Probab., Tome 24 (1996) no. 2, p. 377-398 / Harvested from Project Euclid
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We consider the equation ¶ $$\begin{array}{r@{=}l}u_t \, =\, u_{xx}+ u^\gamma\dot{W}, \quad t>0, \; 0\leq x \leq J,\\[1ex]u(0, x) \, =\, u_0 (x),\\[1ex]u(t, 0) \, = \, u(t, J) =0,\end{array}$$ ¶ where $\dot{W} = \dot{W}(t,x)$ 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 $\gamma$, 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.
Publié le : 1996-01-14
Classification:  Stochastic partial differential equations,  white noise,  heat equation,  initial conditions,  singular,  60H15,  35R60 
@article{1042644721,
     author = {Mueller, Carl},
     title = {Singular initial conditions for the heat equation with a noise
			 term},
     journal = {Ann. Probab.},
     volume = {24},
     number = {2},
     year = {1996},
     pages = { 377-398},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1042644721}
}

Mueller, Carl. Singular initial conditions for the heat equation with a noise
			 term. Ann. Probab., Tome 24 (1996) no. 2, pp.  377-398. http://gdmltest.u-ga.fr/item/1042644721/