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- W4226396807 abstract "We study the compact support property for solutions of the following stochastic partial differential equations: $$partial_t u = a^{ij}u_{x^ix^j}(t,x)+b^{i}u_{x^i}(t,x)+cu+h(t,x,u(t,x))dot{F}(t,x),quad (t,x)in (0,infty)times{bf{R}}^d,$$ where $dot{F}$ is a spatially homogeneous Gaussian noise that is white in time and colored in space, and $h(t, x, u)$ satisfies $K^{-1}|u|^{lambda}leq h(t, x, u)leq K(1+|u|)$ for $lambdain(0,1)$ and $Kgeq 1$. We show that if the initial data $u_0geq 0$ has a compact support, then, under the reinforced Dalang's condition on $dot{F}$ (which guarantees the existence and the Holder continuity of a weak solution), all nonnegative weak solutions $u(t, cdot)$ have the compact support for all $t>0$ with probability 1. Our results extend the works by Mueller-Perkins [Probab. Theory Relat. Fields, 93(3):325--358, 1992] and Krylov [Probab. Theory Relat. Fields, 108(4):543--557, 1997], in which they show the compact support property only for the one-dimensional SPDEs driven by space-time white noise on $(0, infty)times bf{R}$." @default.
- W4226396807 created "2022-05-05" @default.
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- W4226396807 date "2022-01-13" @default.
- W4226396807 modified "2023-09-24" @default.
- W4226396807 title "The compact support property for solutions to the stochastic partial differential equations with colored noise" @default.
- W4226396807 doi "https://doi.org/10.48550/arxiv.2201.04814" @default.
- W4226396807 hasPublicationYear "2022" @default.
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