Mathematical Sciences: Asymptotic Problems for Nonlinear PDE's and Limit Theorems for Random Procesess and Fields

主要研究人员将研究一些 线性和非线性偏微分的渐近问题 方程（PDE）和使用它们的连接的PDE系统 马尔可夫过程。 像波前的运动， 脉冲和半线性抛物系统中的其他结构， 具小扩散系数的椭圆-抛物耦合方程 将被考虑。 从概率的角度来看， 结果将是平均原则类型或中央 极限定理和相应的大偏差型 随机过程 研究人员还将随机研究 演化偏微分方程的扰动。 研究人员计划 发展一个类似于随机扰动理论的理论， 有限维系统 本文给出了非线性系统的多种极限定理， 将考虑由扰动偏微分方程定义的随机场。 主要研究人员将研究一些 线性和非线性偏微分的渐近问题 方程（PDE）和使用它们的连接的PDE系统 马尔可夫过程。 这项工作汇集了两个领域， 数学研究，偏微分方程和 概率论

The principal investigators will study a number of asymptotic problems for linear and nonlinear partial differential equations (PDE's) and systems of PDE's using their connections with Markov processes. Such topics as motion of wave fronts, impulses and other structures in semilinear parabolic systems, coupled elliptic and parabolic equations with small diffusivity will be considered. From a probabilistic point of view the results will be of the averaging principle type or of central limit theorem and large deviation type for the corresponding random processes. The investigators also will study random perturbations of evolutionary PDE's. The investigators plan to develop a theory similar to the theory of random perturbations of finite dimensional systems. Many kinds of limit theorems for the random fields defined by the perturbed PDE's will be considered. The principal investigators will study a number of asymptotic problems for linear and nonlinear partial differential equations (PDE's) and systems of PDE's using their connections with Markov processes. This work brings together two fields of mathematical research, partial differential equations and probability theory.