A new approach to nonlinear partial differential equations

A new perturbative approach to nonlinear partial differential equations

This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation u, + u2(, = u,, the general nonlinear equation u, + u%, = u, is considered and expanded in powers of 6. The coefficients of the S series to sixth order in powers of S is determined and Pad& summation is us...

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 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...

Pseudo-analysis approach to nonlinear partial differential equations

An overview of methods of pseudo-analysis in applications on important classes of nonlinear partial differential equations, occurring in different fields, is given. Hamilton-Jacobi equations, specially important in the control theory, are for important models usually with non-linear Hamiltonian H which is also not smooth, e.g., the absolute value, min or max operations, where it can not apply t...