No Cover Image

E-Thesis 342 views 103 downloads

The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems. / Ameera Nema Al-Kiffai

Swansea University Author: Ameera Nema Al-Kiffai

Abstract

This thesis is concerned with spreading speeds and linear determinacy for both discretetime recursion models Un+1 = Q[un] and reaction-diffusion-convection systems (PDE) under a co-operative assumption. In this thesis we are interested in the role of convection terms in propagation and linear determ...

Full description

Published: 2015
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42766
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2018-08-02T18:55:29Z
last_indexed 2018-08-03T10:11:02Z
id cronfa42766
recordtype RisThesis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2018-08-02T16:24:30.4141983</datestamp><bib-version>v2</bib-version><id>42766</id><entry>2018-08-02</entry><title>The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems.</title><swanseaauthors><author><sid>4725afc8b90fa6911e9fa7959da49d6a</sid><ORCID>NULL</ORCID><firstname>Ameera Nema</firstname><surname>Al-Kiffai</surname><name>Ameera Nema Al-Kiffai</name><active>true</active><ethesisStudent>true</ethesisStudent></author></swanseaauthors><date>2018-08-02</date><abstract>This thesis is concerned with spreading speeds and linear determinacy for both discretetime recursion models Un+1 = Q[un] and reaction-diffusion-convection systems (PDE) under a co-operative assumption. In this thesis we are interested in the role of convection terms in propagation and linear determinacy. Such reaction-diffusion-convection systems have monotone travelling-wave solutions of the form w(x - ct) that describe the propagation of species as a wave with a fixed speed c, connecting two equilibria, a stable equilibrium beta and an unstable equilibrium 0 of the reaction term. The concept of spreading speeds was introduced by Aronson and Weinberger in [2] as a description of asymptotic speeds of spread, and in fact they showed that this spreading speed can be characterized as a minimal travelling wave speed. We discuss a characterization theory of spreading speeds of the PDE system in terms of critical travelling wave speeds. We present sufficient conditions involving both the reaction and convection terms of the PDE system for spreading speeds to equal values obtained from the linearization of the travelling-wave problem of the PDE system about the unstable equilibrium 0. These conditions guarantee the linear determinacy for the discrete-time recursion models and the PDE systems. As a result of the asymmetry in propagation that is caused by the convection terms in the PDE system, and a corresponding lack of reflection invariance in the abstract system un+1 = Q[un], we present separate conditions for non-increasing and non-decreasing initial data, called right and left conditions respectively, and we consider right and left spreading speeds. Weinberger, Lewis and Li in [42] allowed there to be more equilibria other than 0 and beta, in which case different components may spread at different speeds. This implies the need for both slowest and fastest spreading speeds, called right and left slowest (fastest) spreading speeds corresponding, to non-increasing and non-decreasing initial data respectively. We also give sufficient conditions on the reaction and convection terms such that right (left) slowest spreading speed equals right (left) fastest spreading speed for the PDE system, which implies that the system has a right (left) single spreading speed. Examples are included that illustrate the key propositions and theorems, for instance, the existence of reaction and (non-trivial) convection terms for which the right and left linear determinacy conditions are simultaneously satisfied, as well as a system that is right (left) linearly determinate in absence of convection terms, but it is not left linearly determinate in the presence of a convection term.</abstract><type>E-Thesis</type><journal/><journalNumber></journalNumber><paginationStart/><paginationEnd/><publisher/><placeOfPublication/><isbnPrint/><issnPrint/><issnElectronic/><keywords>Applied mathematics.</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2015</publishedYear><publishedDate>2015-12-31</publishedDate><doi/><url/><notes/><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><degreelevel>Doctoral</degreelevel><degreename>Ph.D</degreename><apcterm/><lastEdited>2018-08-02T16:24:30.4141983</lastEdited><Created>2018-08-02T16:24:30.4141983</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Ameera Nema</firstname><surname>Al-Kiffai</surname><orcid>NULL</orcid><order>1</order></author></authors><documents><document><filename>0042766-02082018162520.pdf</filename><originalFilename>10807535.pdf</originalFilename><uploaded>2018-08-02T16:25:20.2870000</uploaded><type>Output</type><contentLength>4695571</contentLength><contentType>application/pdf</contentType><version>E-Thesis</version><cronfaStatus>true</cronfaStatus><embargoDate>2018-08-02T16:25:20.2870000</embargoDate><copyrightCorrect>false</copyrightCorrect></document></documents><OutputDurs/></rfc1807>
spelling 2018-08-02T16:24:30.4141983 v2 42766 2018-08-02 The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems. 4725afc8b90fa6911e9fa7959da49d6a NULL Ameera Nema Al-Kiffai Ameera Nema Al-Kiffai true true 2018-08-02 This thesis is concerned with spreading speeds and linear determinacy for both discretetime recursion models Un+1 = Q[un] and reaction-diffusion-convection systems (PDE) under a co-operative assumption. In this thesis we are interested in the role of convection terms in propagation and linear determinacy. Such reaction-diffusion-convection systems have monotone travelling-wave solutions of the form w(x - ct) that describe the propagation of species as a wave with a fixed speed c, connecting two equilibria, a stable equilibrium beta and an unstable equilibrium 0 of the reaction term. The concept of spreading speeds was introduced by Aronson and Weinberger in [2] as a description of asymptotic speeds of spread, and in fact they showed that this spreading speed can be characterized as a minimal travelling wave speed. We discuss a characterization theory of spreading speeds of the PDE system in terms of critical travelling wave speeds. We present sufficient conditions involving both the reaction and convection terms of the PDE system for spreading speeds to equal values obtained from the linearization of the travelling-wave problem of the PDE system about the unstable equilibrium 0. These conditions guarantee the linear determinacy for the discrete-time recursion models and the PDE systems. As a result of the asymmetry in propagation that is caused by the convection terms in the PDE system, and a corresponding lack of reflection invariance in the abstract system un+1 = Q[un], we present separate conditions for non-increasing and non-decreasing initial data, called right and left conditions respectively, and we consider right and left spreading speeds. Weinberger, Lewis and Li in [42] allowed there to be more equilibria other than 0 and beta, in which case different components may spread at different speeds. This implies the need for both slowest and fastest spreading speeds, called right and left slowest (fastest) spreading speeds corresponding, to non-increasing and non-decreasing initial data respectively. We also give sufficient conditions on the reaction and convection terms such that right (left) slowest spreading speed equals right (left) fastest spreading speed for the PDE system, which implies that the system has a right (left) single spreading speed. Examples are included that illustrate the key propositions and theorems, for instance, the existence of reaction and (non-trivial) convection terms for which the right and left linear determinacy conditions are simultaneously satisfied, as well as a system that is right (left) linearly determinate in absence of convection terms, but it is not left linearly determinate in the presence of a convection term. E-Thesis Applied mathematics. 31 12 2015 2015-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:30.4141983 2018-08-02T16:24:30.4141983 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Ameera Nema Al-Kiffai NULL 1 0042766-02082018162520.pdf 10807535.pdf 2018-08-02T16:25:20.2870000 Output 4695571 application/pdf E-Thesis true 2018-08-02T16:25:20.2870000 false
title The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems.
spellingShingle The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems.
Ameera Nema Al-Kiffai
title_short The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems.
title_full The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems.
title_fullStr The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems.
title_full_unstemmed The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems.
title_sort The role of convection on spreading speeds and linear determinacy for reaction-diffusion-convection systems.
author_id_str_mv 4725afc8b90fa6911e9fa7959da49d6a
author_id_fullname_str_mv 4725afc8b90fa6911e9fa7959da49d6a_***_Ameera Nema Al-Kiffai
author Ameera Nema Al-Kiffai
author2 Ameera Nema Al-Kiffai
format E-Thesis
publishDate 2015
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description This thesis is concerned with spreading speeds and linear determinacy for both discretetime recursion models Un+1 = Q[un] and reaction-diffusion-convection systems (PDE) under a co-operative assumption. In this thesis we are interested in the role of convection terms in propagation and linear determinacy. Such reaction-diffusion-convection systems have monotone travelling-wave solutions of the form w(x - ct) that describe the propagation of species as a wave with a fixed speed c, connecting two equilibria, a stable equilibrium beta and an unstable equilibrium 0 of the reaction term. The concept of spreading speeds was introduced by Aronson and Weinberger in [2] as a description of asymptotic speeds of spread, and in fact they showed that this spreading speed can be characterized as a minimal travelling wave speed. We discuss a characterization theory of spreading speeds of the PDE system in terms of critical travelling wave speeds. We present sufficient conditions involving both the reaction and convection terms of the PDE system for spreading speeds to equal values obtained from the linearization of the travelling-wave problem of the PDE system about the unstable equilibrium 0. These conditions guarantee the linear determinacy for the discrete-time recursion models and the PDE systems. As a result of the asymmetry in propagation that is caused by the convection terms in the PDE system, and a corresponding lack of reflection invariance in the abstract system un+1 = Q[un], we present separate conditions for non-increasing and non-decreasing initial data, called right and left conditions respectively, and we consider right and left spreading speeds. Weinberger, Lewis and Li in [42] allowed there to be more equilibria other than 0 and beta, in which case different components may spread at different speeds. This implies the need for both slowest and fastest spreading speeds, called right and left slowest (fastest) spreading speeds corresponding, to non-increasing and non-decreasing initial data respectively. We also give sufficient conditions on the reaction and convection terms such that right (left) slowest spreading speed equals right (left) fastest spreading speed for the PDE system, which implies that the system has a right (left) single spreading speed. Examples are included that illustrate the key propositions and theorems, for instance, the existence of reaction and (non-trivial) convection terms for which the right and left linear determinacy conditions are simultaneously satisfied, as well as a system that is right (left) linearly determinate in absence of convection terms, but it is not left linearly determinate in the presence of a convection term.
published_date 2015-12-31T03:53:36Z
_version_ 1763752664661753856
score 11.036706

Similar Items