Comparison principle for some nonlocal 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...

Pontryagin's Minimum Principle for Fuzzy Optimal Control Problems

The objective of this article is to derive the necessary optimality conditions, known as Pontryagin's minimum principle, for fuzzy optimal control problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its $alpha$-level sets.

On the balancing principle for some problems of Numerical Analysis

We discuss a choice of weight in penalization methods. The motivation for the use of penalization in Computational Mathematics is to improve the conditioning of the numerical solution. One example of such improvement is a regularization, where a penalization substitutes ill-posed problem for wellposed one. In modern numerical methods for PDE a penalization is used, for example, to enforce a con...

St Reading on Some Nonlocal Variational Problems 3

We study uniqueness and non uniqueness of minimizers of functionals involving nonlocal 17 quantities. We give also conditions which lead to a lack of minimizers and we show how minimization on an infinite dimensional space reduces here to a minimization on R. 19 Among other things, we prove that uniqueness of minimizers of functionals of the form R Ω a(R Ω gu dx)|∇u| 2 dx − 2 R Ω fu dx is ensur...

Positive Solutions of Some Nonlocal Boundary Value Problems