The existence, uniqueness, and global exponential stability of traveling wave solutions of a class of nonlinear and nonlocal evolution equations are established. It is assumed that there are two stable equilibria so that a tr aveling wave is a solution that connects them. A basic assumption is the comparison principle: a smaller initial value produces a smaller solution. When applied to di eren...

In this thesis we study numerical methods for simulating mechanical deformations of cell membranes. Such models are given in terms of fourth order partial di erential equations. In order to enable comparisons of the models predictions to experimental results, the equations must be solved on arbitrary cell geometries. A Finite Element Method based on subdivision surfaces, which is capable of dis...

Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equation...

In this paper we discuss stochastic di erential delay equations with Markovian switching. Such an equation can be regarded 9 as the result of several stochastic di erential delay equations switching from one to another according to the movement of a Markov chain. The aim of this paper is to investigate the stability in distribution of the equations. 11 c © 2003 Published by Elsevier Science B.V.

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in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population of discrete individuals characterized by one or several adaptive traits. The population is modelled as a stochastic point process whose generator captures t...

An approach for transforming systems of partial di erential equations in order to obtain new formulations which are more accessible to numerical solution is studied. An algorithm is developed for generating such transformations automatically, using symbolic computations employing Gr obner bases. The algorithm is implemented using freely available software. This approach, along with planned dev...

We de ne a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of di erential delay equations possessing a feedback condition. This extends analogous de nitions for cyclic systems of ODE's, and for scalar di erential delay equations. We relate the values of V to the real parts of the Floquet multipliers for such linear periodic systems, and thereby prove all Floque...

Einstein's eld equations for spatially self-similar locally rotationally symmetric perfect uid models are investigated. The eld equations are rewritten as a rst order system of autonomous ordinary di erential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system of di erential equations is reduced as far as possible. The system is subsequ...