Nonlinear Differential Equations in Preventing Financial Risks

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...

Nonlinear Ordinary Differential Equations

Most physical processes are modeled by differential equations. First order ordinary differential equations, also known as dynamical systems, arise in a wide range of applications, including population dynamics, mechanical systems, planetary motion, ecology, chemical diffusion, etc., etc. See [19, 72,ODES] for additional material and applications. The goal of this chapter is to study and solve i...

Nonlinear Partial Differential Equations

Nonlinear Partial Differential Equations

The ultimate topic to be touched on in this book is the vast and active field of nonlinear partial differential equations. Leaving aside quantum mechanics, which remains to date an inherently linear theory, most real-world physical systems, including gas dynamics, fluid mechanics, elasticity, relativity, ecology, neurology, thermodynamics, and many more, are modeled by nonlinear partial differe...

Nonlinear Differential Equations

1. Introduction. A few nonlinear differential equations have known exact solutions, but many which are important in applications do not. Sometimes these equations may be linearized by an expansion process in which nonlinear terms are discarded. When nonlinear terms make vital contributions to the solution this cannot be done, but sometimes it is enough to retain a few "small" ones. Then a pertu...