发表机构
Auburn University（奥本大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究由对称 $\alpha$-稳定 Lévy 白噪声驱动的非 Lipschitz 系数随机热方程，构造了负 Sobolev 空间中的弱解及可预测温和解，并证明温和解为弱解的密度。
AI 中文摘要
我们研究有界区间上具有零 Dirichlet 边界条件、由对称 $\alpha$-稳定时空 Lévy 白噪声驱动的随机热方程，其中 $1<\alpha<2$。漂移系数和噪声系数均为连续且至多线性增长。对于有界确定性初值和每个 $r>1/2$，我们在负 Sobolev 空间 $\mathbb{H}_{-r}$ 中构造具有 càdlàg 路径的弱解。我们还在相同的随机基和相同的噪声下构造一个可预测的温和解。在每个固定的确定性时刻，该温和解是分布值弱解的密度。
英文摘要
We study the stochastic heat equation on a bounded interval with zero Dirichlet boundary conditions, driven by symmetric $α$-stable space--time Lévy white noise, where $1<α<2$. Both the drift and noise coefficients are continuous and have at most linear growth. For bounded deterministic initial data and every $r>1/2$, we construct a weak solution with càdlàg paths in the negative Sobolev space $\mathbb{H}_{-r}$. We also construct a predictable mild solution on the same stochastic basis and with the same noise. At each fixed deterministic time, this mild solution is a density of the distribution-valued weak solution.
Comments45 pages
