On two new functional equations for generalized Joukowski transformations

3D Mappings by Generalized Joukowski Transformations

The classical Joukowski transformation plays an important role in different applications of conformal mappings, in particular in the study of flows around the so-called Joukowski airfoils. In the 1980s H. Haruki and M. Barran studied generalized Joukowski transformations of higher order in the complex plane from the view point of functional equations. The aim of our contribution is to study the...

On a new method for finding generalized equivalence transformations for differential equations involving arbitrary functions

A new efficient method for finding the generalized equivalence transformations related to a differential equation system via its extended classical symmetries is presented. This technique applies to the case when the arbitrary functions involve only the independent variables of the system. Intriguingly, for this type of equations, any symbolic manipulation program designed to find classical Lie...

The Taylor Method for Numerical Solution of Fuzzy Generalized Pantograph Equations with Linear Functional Argument

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...

On two functional equations and their solutions

The present work aims to determine the solution f : R2 → R of the equation f(ux − vy, uy − vx) = f(x, y) + f(u, v) + f(x, y) f(u, v) for all x, y, u, v ∈ R without any regularity assumption. The solution of the functional equation f(ux+ vy, uy− vx) = f(x, y) + f(u, v) + f(x, y) f(u, v) is also determined. The methods of solution of these equations are simple and elementary. These two equations ...