论文标题
一类各向异性随机退化抛物线抛物性hyperbolic方程的边界价值问题
A Boundary Value Problem for a Class of Anisotropic Stochastic Degenerate Parabolic-Hyperbolic Equations
论文作者
论文摘要
我们在空间域上建立了混合类型的初始型非线性抛物线式 - 混合型 - co = \ co = \ co'\ x \ co''$在$ \ po \ po \ po \ co'\ co'\ x \ co中强加于“ noumann边界的条件”上，并且在超级方面的条件上强加于“超质量边界”的情况，我们建立了混合抛物线型抛物线型 - 抛物线式 - 柔软的方程式的最初实物价值问题。 $ \ co'\ x \ po \ co” $，抛物线边界。在我们对这个问题的分析中，还需要强调的是，我们提到了此处研究的新的强痕迹定理，用于随机非线性抛物线抛物线的特殊类别，这对于动力学解决方案的唯一性以及新的平均方程式平均方程类别的唯一性具有决定性的作用，这是强大的强度属性的重要方程组。我们还提供了近似非化学问题的详细分析，据作者所知，这也是第一次在这里进行的，我们证明其解决方案将其收敛到我们初始有限价值问题的解决方案。
We establish the well-posedness of an initial-boundary value problem of mixed type for a stochastic nonlinear parabolic-hyperbolic equation on a space domain $\cO=\cO'\X\cO''$ where a Neumann boundary condition is imposed on $\po\cO'\X\cO"$, the hyperbolic boundary, and a Dirichlet condition is imposed on $\cO'\X\po\cO"$, the parabolic boundary. Among other points to be highlighted in our analysis of this problem we mention the new strong trace theorem for the special class of stochastic nonlinear parabolic-hyperbolic equations studied here, which is decisive for the uniqueness of the kinetic solution, and the new averaging lemma for the referred class of equations which is a vital part of the proof of the strong trace property. We also provide a detailed analysis of the approximate nondegenerate problems, which is also made here for the first time, as far as the authors know, whose solutions we prove to converge to the solution of our initial-boundary value problem.
