Cyclic animation using partial differential equations

Using Partial Differential Equations

A different approach is developed to study self-similar solutions in Bianchi type III spacetimes. Self-similar solutions in both tilted and non tilted cases are obtained. By solving a system of six non linear and inhomogeneous partial differential equations. It is shown that in non-tilted case the above space-times admit orthogonal zero kind self-similarity and in tilted case. It admits second ...

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...

Discrete surface modelling using partial differential equations

We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows. These nonlinear equations are discretized based on discrete differential geometry operators. ...

Partial Differential Equations Midterm

1), find the explicit fundamental solution to the heat equation ∆u + b · ∇u − u t = 0 in R n × (0, ∞). (1) Letting G be what you find, show u 0 (x) = lim t→0 + R n G(x, t; y, 0)u 0 (y) dy, (2) when u 0 is bounded and continuous on R n. Taking the Fourier transform (with respect to x) of the equation gives −|ξ| 2 ˆ u + ib · ξ ˆ u − ˆ u t = 0 − |ξ| 2 + ib · ξ ˆ u = ˆ u t =⇒û = ce −(|ξ| 2 +ib·ξ)t ...

Stochastic Partial Differential Equations