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On the support of solutions to the heat equation with noise. (English) Zbl 0749.60057
Let $$U(t,x)$$ be a solution of the stochastic partial differential equation $$U_ t=U_{xx}+U^ \gamma \dot W$$, where $$\gamma\geq 1$$, $$\dot W$$ is a 2-parameter white noise. If $$U(0,x)$$ is bounded, nonnegative, with compact support and not identically $$0$$, then with probability 1, $$U(t,x)>0$$ for all $$t>0$$, $$x\in R$$.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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