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On monotone and Schwarz alternating methods for nonlinear elliptic PDEs

Shiu-Hong Lui (2001)

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

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...

On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs

Shiu-Hong Lui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...

On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay

S. Ruan (2009)

Mathematical Modelling of Natural Phenomena

In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations...

On the age-dependent predator-prey model

Antoni Leon Dawidowicz, Anna Poskrobko, Jerzy Leszek Zalasiński (2011)

Applicationes Mathematicae

The paper deals with the description of a model which is the synthesis of two classical models, the Lotka-Volterra and McKendrick-von Foerster models. The existence and uniqueness of the solution for the new population problem are proved, as well the asymptotic periodicity but under some simplifying assumptions.

On the Dynamics of a Two-Strain Influenza Model with Isolation

F. Chamchod, N.F. Britton (2012)

Mathematical Modelling of Natural Phenomena

Influenza has been responsible for human suffering and economic burden worldwide. Isolation is one of the most effective means to control the disease spread. In this work, we incorporate isolation into a two-strain model of influenza. We find that whether strains of influenza die out or coexist, or only one of them persists, it depends on the basic reproductive number of each influenza strain, cross-immunity between strains, and isolation rate. We propose criteria that may be useful for controlling...

On the dynamics of a vaccination model with multiple transmission ways

Shu Liao, Weiming Yang (2013)

International Journal of Applied Mathematics and Computer Science

In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity....

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