Perturbation Solutions on J-Integral for Nonlinear Crack 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...

Solutions of Nonlinear Integral Equations and Their Application to Singular Perturbation Problems Thesis By

Sufficient conditions for the existence and uniqueness, and estimates, of a continuous vector solution y = y(t) to the integral equation y(t) = u(t) + EL(t) Ef t M(s) f(s,y(s)) ds + K(t,s) f(s,y(s)) ds, t 0 are derived. A successive approximation technique involving a double sequence is used in the proof . This integral equation result is applied to the second order singular perturbation proble...

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

On a Nonlinear Integral Equation with Contractive Perturbation

Integral Equation Methods and Numerical Solutions of Crack and Inclusion Problems in Planar Elastostatics

We present algorithms for the crackand inclusion problem in planar linear elastostatics. The algorithms are based on new integral equations. For the pure crack problem the integral equations are of Fredholm’s second kind. Our algorithms show great stability and allow for solutions to problems more complex than previously has been possible. Our results are orders of magnitudes more accurate than...