论文标题
随机分数保护法
Stochastic fractional conservation laws
论文作者
论文摘要
在本文中，我们考虑了由多种噪声驱动的非线性分数保护定律的库奇问题。特别是，我们关注适当的理论以及对这些方程式解决方案的长期行为的研究。我们使用消失的粘度法显示了所需的动力学溶液的存在。实际上，我们建立了近似粘性溶液与动力学溶液的强烈收敛。此外，在非线性扩张条件下，我们使用众所周知的Krylov-Bogoliubov定理证明了不变的度量的存在。最后，我们展示了不变度量的独特性和奇异性。
In this paper, we consider the Cauchy problem for the nonlinear fractional conservation laws driven by a multiplicative noise. In particular, we are concerned with the well-posedness theory and the study of the long-time behavior of solutions for such equations. We show the existence of desired kinetic solution by using the vanishing viscosity method. In fact, we establish strong convergence of the approximate viscous solutions to a kinetic solution. Moreover, under a nonlinearity-diffusivity condition, we prove the existence of an invariant measure using the well-known Krylov-Bogoliubov theorem. Finally, we show the uniqueness and ergodicity of the invariant measure.
