In this paper, a numerical method is presented for proving the existence and inclusion of connecting orbits of continuous dynamical systems described by parameterized nonlinear ordinary di erential equations. Taking a certain second order nonlinear ordinary di erential equaiton as an example, the existence of homoclinic bifurcation points is proved by the method.

The transient drift di usion model describing the charge transport in semiconductors is con sidered Poisson s equation which is usually used is replaced by Maxwell s equations The di usion and mobility coe cients and the dielectric and magnetic susceptibilities may depend on the space variables Global existence and convergence to the thermal equilibrium is shown

We consider a reaction–di usion equation in a bounded domain O⊂Rd, driven by a space– time white noise, with a drift term having polynomial growth and a di usion term which is not boundedly invertible, in general. We are showing that the transition semigroup corresponding to the equation has a regularizing e ect. More precisely, we show that it maps bounded and Borel functions de ned in the Hil...

The production of modern microchips requires a large number of fabrication steps. One important step is the creation of semiconducting areas, where charged dopants are implanted into a semiconducting material and under the in uence of high temperatures the dopants penetrate into the layer. This redistribution of dopants and point defects can be described in terms of pair di usion mechanisms. Th...

This report discusses a mathematical software package DKLAG5 which consists of a suite of FORTRAN subroutines for the numerical solution of systems of functional di erential equations with state dependent delays. The package implements continuously imbedded Runge{ Kutta methods which are based on C polynomial interpolants. These interpolants are exploited by the software to handle the necessary...

A parallel algorithm, which is derived directly from the Schwarz alternating algorithm with an overlapping domain decomposition, for solving boundary value problems of elliptic partial di€erential equations is analyzed. A new general analysis framework di€erent from Lions' ones is established to describe the recursive relations of error functions between approximate solutions and the exact solu...

We synthesize robust nonlinear static output feedback controllers for systems of quasi-linear parabolic partial di!erential equations with time-dependent spatial domains and uncertain variables. The controllers are successfully applied to a typical di!usion}reaction process with moving boundary and uncertainty. ( 2000 Elsevier Science Ltd. All rights reserved.

The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by di erential equations with discontinuous right{hand sides. In this paper we analyze the behavior of three di erent Lotka{Volterra predator{prey systems with opt...

We announce publicly available Fortran software for the initial value problem IVP in ordinary di erential equations ODEs We describe the interfaces and how Fortran language features a ord the opportunity both to address di erent types and structures of variables and to provide functionality not usually directly associated with IVP solvers

In this paper, we study the existence and stability of traveling waves in lattice dynamical systems, in particular, in lattice ordinary di erential equations (lattice ODE's) and in coupled map lattices (CML's). Instead of employing the moving coordinate approach as for partial di erential equations, we construct a local coordinate system around a traveling wave solution of a lattice ODE, analog...