Boundary behavior and interior Hölder regularity of solution to nonlinear stochastic partial differential equations driven by space-time white noise
Year: 2019
Type: preprint
Abstract: We present uniqueness and existence in weighted Sobolev spaces of the equation $$ u_t=(au_{xx}+bu_x+cu)+ ξ|u|^{1+λ} {\dot{B}}, \quad\,\, t>0, \, x\in (0,1) $$ with initial data $u(0,\cdot)=u_0$ and zero boundary data. Here $λ\in [0,1/2)$, $\dot{B}$ is a space-time white noise, and the coefficients $a,b,c$ and the function $ξ$ depend on $(ω,t,x)$ and the initial data $u_0$ depends on $(ω,x)$. More importantly, we obtain various interior Hölder regularities and boundary behaviors of the solution. For instance, if the initial data is in appropriate $L_p$ spaces, then for any small $\varepsilon>0$ and $T
Source: arXiv (Cornell University)
Authors: Han, Beom-seok, Kim, Kyeong-hun
Institution: Korea University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2654423792, G2754275335
OpenAlex ID: W2947393336