标题： 双曲系统带有随机场系数的广义解 显示英文标题

标题： Generalized solutions to hyperbolic systems with random field coefficients

摘要： 本文研究了一维空间中具有随机场系数的线性双曲系统。在许多应用中，要求系数路径的正则性较低，这超出了经典随机分析的范围。因此，我们将分析置于Colombeau广义函数代数的框架内。我们获得了Colombeau随机过程的新表征，并在此框架内建立了解的存在性和唯一性。给出了对随机波和传输方程的一些应用，并将Colombeau解与经典弱解相关联，当后者存在时。 显示英文摘要

摘要： The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic analysis. For this reason, we place our analysis in the framework of Colombeau algebras of generalized functions. We obtain new characterizations of Colombeau stochastic processes and establish existence and uniqueness of solutions in this framework. A number of applications to stochastic wave and transport equations are given and the Colombeau solutions are related to classical weak solutions, when the latter exist.