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Waves in reaction-transport systems with memory and long-distance dispersal effects

具有记忆和长距离扩散效应的反应传递系统中的波

基本信息

批准号：
EP/D03115X/1
负责人：
Sergei Fedotov
金额：
$ 1.31万
依托单位：
University of Manchester
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FD03115X%2F1
关键词：
Waves reaction transport systems memory

项目摘要

Why do we need to develop the theory of wave propagation into an unstable state for systems of integro-differential and integro-difference equations? Because they provide more realistic models for various phenomena in physics, chemistry, biology. It is well known that a macroscopic transport process comes from the overall effect of many particles performing complex random movements. Classical diffusion is just an approximation to this transport in the long-time, large-distance parabolic limit, but a diffusion approximation is not always appropriate for problems involving propagating fronts. From a practical point of view, this implies that models in physics,mathematical biology, etc. cannot be expected to work properly, in general, if they are based on simple reaction-diffusion ideas. Hence it is desirable to extend these results by considering more suitable, alternative models for transport processes based on integro-differential and integro-difference equations. Very recently there have been some important developments in the theory of wave propagation for a single integro-differential equation. We now wish to extend this groundwork to the solution of systems of integro-differential and integro-difference equations. An advantage is that we will be able to take into account: (i) realistic multi-component cases; (ii) long-range and time-delayed interactions; (iii) long-distance dispersal. Memory effects and long-distance dispersal are a significant feature in many areas of physics, chemistry and biology, but they are often ignored because techniques are not yet readily available for dealing with them. We plan to address this deficiency.

为什么我们需要把波的传播理论发展成积分-微分和积分-差分方程组的不稳定状态？因为它们为物理、化学、生物学中的各种现象提供了更现实的模型。众所周知，宏观输运过程来自于许多粒子进行复杂随机运动的总体效应。经典扩散只是在长时间、长距离抛物线极限下这种输运的近似值，但扩散近似值并不总是适用于涉及传播锋的问题。从实际的角度来看，这意味着物理学、数学生物学等领域的模型，如果基于简单的反应扩散思想，一般来说，就不能指望它们能正常工作。因此，通过考虑更合适的、基于积分-微分和积分-差分方程的输运过程的替代模型来扩展这些结果是可取的。最近，单积分-微分方程的波传播理论有了一些重要的进展。现在我们希望把这个基础扩展到积分微分方程组和积分差分方程组的解上。一个优点是，我们将能够考虑到：(i)实际的多组件情况；（ii）远距离和延时的相互作用；（三）远距离扩散。记忆效应和远距离扩散是物理、化学和生物学许多领域的一个重要特征，但它们常常被忽视，因为处理它们的技术尚不成熟。我们计划解决这一缺陷。