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Meandering of trajectories of polynomial vector fields in the affine n-space.

Dimitri Novikov, Sergei Yakovenko (1997)

Publicacions Matemàtiques

We give an explicit upper bound for the number of isolated intersections between an integral curve of a polynomial vector field in Rn and an affine hyperplane.The problem turns out to be closely related to finding an explicit upper bound for the length of ascending chains of polynomial ideals spanned by consecutive derivatives.This exposition constitutes an extended abstract of a forthcoming paper: only the basic steps are outlined here, with all technical details being either completely omitted...

Mixed type semicontinuous differential inclusions in Banach spaces

Tzanko Donchev (2001)

Annales Polonici Mathematici

We consider a class of differential inclusions in (nonseparable) Banach spaces satisfying mixed type semicontinuity hypotheses and prove the existence of solutions for a problem with state constraints. The cases of dissipative type conditions and with time lag are also studied. These results are then applied to control systems.

Modelling tumour-immunity interactions with different stimulation functions

Petar Zhivkov, Jacek Waniewski (2003)

International Journal of Applied Mathematics and Computer Science

Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different...

Multiple spatial scales in engineering and atmospheric low Mach number flows

Rupert Klein (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The first part of this paper reviews the single time scale/multiple length scale low Mach number asymptotic analysis by Klein (1995, 2004). This theory explicitly reveals the interaction of small scale, quasi-incompressible variable density flows with long wave linear acoustic modes through baroclinic vorticity generation and asymptotic accumulation of large scale energy fluxes. The theory is motivated by examples from thermoacoustics and combustion. In an almost obvious way specializations of this...

Multiple spatial scales in engineering and atmospheric low Mach number flows

Rupert Klein (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The first part of this paper reviews the single time scale/multiple length scale low Mach number asymptotic analysis by Klein (1995, 2004). This theory explicitly reveals the interaction of small scale, quasi-incompressible variable density flows with long wave linear acoustic modes through baroclinic vorticity generation and asymptotic accumulation of large scale energy fluxes. The theory is motivated by examples from thermoacoustics and combustion. In an almost obvious way specializations of...

N -widths for singularly perturbed problems

Martin Stynes, R. Bruce Kellogg (2002)

Mathematica Bohemica

Kolmogorov N -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the N -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.

Novel method for generalized stability analysis of nonlinear impulsive evolution equations

JinRong Wang, Yong Zhou, Wei Wei (2012)

Kybernetika

In this paper, we discuss some generalized stability of solutions to a class of nonlinear impulsive evolution equations in the certain piecewise essentially bounded functions space. Firstly, stabilization of solutions to nonlinear impulsive evolution equations are studied by means of fixed point methods at an appropriate decay rate. Secondly, stable manifolds for the associated singular perturbation problems with impulses are compared with each other. Finally, an example on initial boundary value...

Currently displaying 181 – 200 of 430