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Global solution for superlinear stochastic heat equation on $\mathbb{R}^d$ under Osgood-type conditions
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abstract
We study the \textit{stochastic heat equation} (SHE) on $\R^d$ subject to a centered Gaussian noise that is white in time and colored in space.The drift term is assumed to satisfy an Osgood-type condition and the diffusion coefficient may have certain related growth. We show that there exists random field solution which do not explode in finite time. This complements and improves upon recent results on blow-up of solutions to stochastic partial differential equations.
Forward citations
Cited by 2 Pith papers
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On the well-posedness of SPDEs with locally Lipschitz coefficients
Under slow-growth conditions on the local Lipschitz constants, the stochastic heat equation on the real line has a unique solution with finite moments of all orders.
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A stochastic heat equation with non-locally Lipschitz coefficients
For the stochastic heat equation on the torus with coefficients growing like u|log u|^A near zero (A<1 for drift, A<1/4 for noise), a unique global strictly positive mild solution exists.
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