Martingale solutions and Markov selections for 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...

Stochastic Partial Differential Equations

Solutions of Backward Stochastic Differential Equations on Markov Chains

Consider a continuous time, finite state Markov chain X = {Xt, t ∈ [0, T ]}. We identify the states of this process with the unit vectors ei in R N , where N is the number of states of the chain. We consider stochastic processes defined on the filtered probability space (Ω, F , {Ft}, P), where {Ft} is the completed natural filtration generated by the σ-fields Ft = σ({Xu, u ≤ t}, F ∈ FT : P(F ) ...

Smooth Solutions of Non-linear Stochastic Partial Differential Equations

Abstract. In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau’s equations on the real line, stochastic 2D Navier-Stokes equations in the whole space and a stochastic tamed 3D Navier-Stokes ...

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations