Well-Posedness and Stability Results for Some Periodic Muskat Problems

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...

Well-posedness of the Muskat problem with H2 initial data

Article history: Received 30 December 2014 Accepted 13 August 2015 Available online xxxx Communicated by Charles Fefferman MSC: 35R35 35Q35 35S10 76B03

Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: the periodic case

We prove that the KdV-Burgers is globally well-posed in H−1(T) with a solution-map that is analytic fromH−1(T) to C([0, T ];H−1(T)) whereas it is ill-posed in Hs(T), as soon as s < −1, in the sense that the flow-map u0 7→ u(t) cannot be continuous from H s(T) to even D′(T) at any fixed t > 0 small enough. In view of the result of Kappeler and Topalov for KdV it thus appears that even if the dis...

Well-posedness for Hyperbolic Problems

Stability Results for Some Periodic Feedback Controllers

We propose two periodic feedback schemes for the stabilization of periodic orbits for one dimensional discrete time chaotic systems. These schemes can be generalized to higher dimensional systems in a straightforward way. We show that the proposed schemes achieve stabilization of a wide range of periodic orbits. The proposed schemes are quite simple and we show that any hyperbolic periodic orbi...