A duality analysis on stochastic partial differential equations

A Primer on Stochastic Partial Differential Equations

These notes form a brief introductory tutorial to elements of Gaussian noise analysis and basic stochastic partial differential equations (SPDEs) in general, and the stochastic heat equation, in particular. The chief aim here is to get to the heart of the matter quickly. We achieve this by studying a few concrete equations only. This chapter provides sufficient preparation for learning more adv...

Stochastic Partial Differential Equations

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...

On quasi-linear stochastic partial differential equations

We prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.

NSF/CBMS Conference Analysis of Stochastic Partial Differential Equations

Ten Lectures on Analysis of Stochastic Partial Differential Equations, Davar Khoshnevisan (University of Utah) The following is a more detailed plan for the lectures.