论文标题
噪声的分数退化抛物线式铜牛肉问题
A fractional degenerate parabolic-hyperbolic Cauchy problem with noise
论文作者
论文摘要
我们认为在任何空间维度，非本地，非线性且可能是退化扩散项的空间维度下，随机标量抛物线式纤维方程的Cauchy问题。这些方程是非本地的，因为它们涉及分数扩散算子。我们适应了随机熵解决方案的概念，并提供了一个新的技术框架来证明独特性。存在证明依赖于消失的粘度法。此外，使用有界变异（BV）估计值消失的粘度近似值，我们得出了对非线性的显式连续依赖估计，并得出了随机消失的粘度方法的误差估计。此外，对于更通用的方程式，我们开发了唯一方法“ a la kruzkov”，其中噪声系数可能明确取决于空间变量。
We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators. We adapt the notion of stochastic entropy solution and provide a new technical framework to prove the uniqueness. The existence proof relies on the vanishing viscosity method. Moreover, using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities and derive error estimate for the stochastic vanishing viscosity method. In addition, we develop uniqueness method "a la Kruzkov" for more general equations where the noise coefficient may depends explicitly on the spatial variable.
