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Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion

M. Alfaro, D. Hilhorst (2010)

Mathematical Modelling of Natural Phenomena

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.

Generic principles of active transport

Mauro Mobilia, Tobias Reichenbach, Hauke Hinsch, Thomas Franosch, Erwin Frey (2008)

Banach Center Publications

Nonequilibrium collective motion is ubiquitous in nature and often results in a rich collection of intriguing phenomena, such as the formation of shocks or patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase transitions. These stochastic many-body features characterize transport processes in biology, soft condensed matter and, possibly, also in nanoscience. Inspired by these applications, a wide class of lattice-gas models has recently been considered. Building on the celebrated...

Genetic and Tabu search algorithms for peptide assembly problem

Jacek Błażewicz, Marcin Borowski, Piotr Formanowicz, Tomasz Głowacki (2010)

RAIRO - Operations Research

Determining amino acid sequences of protein molecules is one of the most important issues in molecular biology. These sequences determine protein structure and functionality. Unfortunately, direct biochemical methods for reading amino acid sequences can be used for reading short sequences only. This is the reason, which makes peptide assembly algorithms an important complement of these methods. In this paper, a genetic algorithm solving the problem of short amino acid sequence assembly is presented....

Global Asymptotic Stability of Equilibria in Models for Virus Dynamics

J. Prüss, R. Zacher, R. Schnaubelt (2008)

Mathematical Modelling of Natural Phenomena

In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibrium which takes over this...

Global attractivity of the equilibrium of a nonlinear difference equation

John R. Graef, C. Qian (2002)

Czechoslovak Mathematical Journal

The authors consider the nonlinear difference equation x n + 1 = α x n + x n - k f ( x n - k ) , n = 0 , 1 , ⋯ . 1 where α ∈ ( 0 , 1 ) , k ∈ { 0 , 1 , ⋯ } and f ∈ C 1 [ [ 0 , ∞ ) , [ 0 , ∞ ) ] ( 0 ) with f ' ( x ) < 0 . They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.

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