Hörmander’s theorem for stochastic partial differential equations

The Substitution Theorem for Semilinear Stochastic Partial Differential Equations

Abstract. In this article we establish a substitution theorem for semilinear stochastic evolution equations (see’s) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techni...

The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations∗

The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2. In Part 1, we prove...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Stochastic Partial Differential Equations

Algorithm Refinement for Stochastic Partial Differential Equations

We construct a hybrid particle/continuum algorithm for linear diffusion in the fluctuating hydrodynamic limit. The particles act as independent random walkers and the fluctuating diffusion equation is solved by a finite difference scheme. At the interface between the particle and continuum computations the coupling is by flux matching, and yields exact mass conservation. This approach is an ext...