On Elliptic Partial Differential Equations and Uniqueness Theorems for Closed Surfaces

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...

Lecture Notes on Elliptic Partial Differential Equations

Existence and Uniqueness Theorems for Fuzzy Differential Equations

Fuzzy differential equation is an important tool to deal with dynamic systems in fuzzy environments. However, it is difficult to find the solutions to all fuzzy differential equations. In this paper, methods to solve linear fuzzy differential equations and reducible fuzzy differential equations are given. Moreover, existence and uniqueness theorem for homogeneous fuzzy differential equations ar...

Uniqueness Theorems for Ordinary Differential Equations with Hölder Continuity

We establish some uniqueness results near 0 for ordinary differential equations of the type u(t) = f(u(t)) which satisfies u(0) = u′(0) = · · · = u(m−1)(0) = 0 and u(0) 6= 0 with m ≥ n. We also show that although f is not Lipschitz near 0, it is always Hölder continuous.

On the Exact Solution for Nonlinear Partial Differential Equations

In this study, we aim to construct a traveling wave solution for nonlinear partial differential equations. In this regards, a cosine-function method is used to find and generate the exact solutions for three different types of nonlinear partial differential equations such as general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKDV) and general equal width wave equ...