Travelling Waves in Monostable and Bistable Stochastic Partial Differential Equations

Travelling Waves in Continuum/discrete Bistable/monostable Dynamics

Traveling waves play a key role in mathematical models since they characterize observable fundamental phenomena in nature. A typical traveling wave corresponds to a state which is time independent (in some cases time periodic) in a moving coordinates. In a one space dimensional setting, it depends only on z := x − ct where c is the wave speed and x and t are respectively space and time variable...

Bistable travelling waves for nonlocal reaction diffusion equations

We are concerned with travelling wave solutions arising in a reaction diffusion equation with bistable and nonlocal nonlinearity, for which the comparison principle does not hold. Stability of the equilibrium u ≡ 1 is not assumed. We construct a travelling wave solution connecting 0 to an unknown steady state, which is “above and away” from the intermediate equilibrium. For focusing kernels we ...

Stochastic Partial Differential Equations

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...

Exact travelling wave solutions for some complex nonlinear partial differential equations

This paper reflects the implementation of a reliable technique which is called $left(frac{G'}{G}right)$-expansion  ethod for  constructing exact travelling wave solutions of nonlinear partial  differential equations. The proposed algorithm has been successfully tested on two two selected equations, the balance numbers of which are not positive integers namely Kundu-Eckhaus equation and  Derivat...