Stochastic viscosity solutions for nonlinear stochastic partial differential equations. Part II

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

Topological soliton solutions of the some nonlinear partial differential equations

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...

Stationary Solutions of Stochastic Differential Equation with Memory and Stochastic Partial Differential Equations

We explore Itô stochastic differential equations where the drift term has possibly infinite dependence on the past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proved if the dependence on the past decays sufficiently fast. The results of this paper ar...

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 ...