Vector fields and differential equations

Differential Equations with singular fields

This paper investigates the well posedness of ordinary differential equations and more precisely the existence (or uniqueness) of a flow through explicit compactness estimates. Instead of assuming a bounded divergence condition on the vector field, a compressibility condition on the flow (bounded jacobian) is considered. The main result provides existence under the condition that the vector fie...

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...

Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations

This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of λ-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetries with approaches that had been previously introduced: the exponential vector fields and the λ-...

Differential Equations on the two dimensional torus 1 Constant vector fields on the torus

Large Deviations for Stochastic Differential Equations on S Associated with the Critical Sobolev Brownian Vector Fields

The purpose of our paper is to prove a large deviation principle on the asymptotic behavior of the stochastic differential equations on the sphere S associated with a critical Sobolev Brownian vector field which was constructed by Fang and Zhang 1 . Recall that Schilder theorem states that if B is the real Brownian motion and C0 0, 1 is the space of real continuous functions defined on 0, 1 , n...