Talagrand concentration inequalities 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

Lyapunov inequalities for partial differential equations ✩

This paper is devoted to the study of Lp Lyapunov-type inequalities (1 p +∞) for linear partial differential equations. More precisely, we treat the case of Neumann boundary conditions on bounded and regular domains in RN . It is proved that the relation between the quantities p and N/2 plays a crucial role. This fact shows a deep difference with respect to the ordinary case. The linear study i...

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...

Postprocessing for Stochastic Parabolic Partial Differential Equations

We investigate the strong approximation of stochastic parabolic partial differential equations with additive noise. We introduce post-processing in the context of a standard Galerkin approximation, although other spatial discretizations are possible. In time, we follow [20] and use an exponential integrator. We prove strong error estimates and discuss the best number of postprocessing terms to ...