E-Thesis 501 views 107 downloads
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion / YINI DU
Swansea University Author: YINI DU
DOI (Published version): 10.23889/SUthesis.60766
Abstract
In this thesis, we present an approach to characterising fast-reaction lim-its of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary dif-ferential equation on unbounded domains. Here, we replace the terms of the...
Published: |
Swansea
2022
|
---|---|
Institution: | Swansea University |
Degree level: | Doctoral |
Degree name: | Ph.D |
Supervisor: | Crooks, Elaine ; Mercuri, Carlo |
URI: | https://cronfa.swan.ac.uk/Record/cronfa60766 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
first_indexed |
2022-08-05T15:29:17Z |
---|---|
last_indexed |
2023-01-13T19:21:08Z |
id |
cronfa60766 |
recordtype |
RisThesis |
fullrecord |
<?xml version="1.0"?><rfc1807><datestamp>2022-08-05T16:41:34.6879800</datestamp><bib-version>v2</bib-version><id>60766</id><entry>2022-08-05</entry><title>Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion</title><swanseaauthors><author><sid>2bfcd9725f897025ac9db0056fd3dc64</sid><firstname>YINI</firstname><surname>DU</surname><name>YINI DU</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2022-08-05</date><abstract>In this thesis, we present an approach to characterising fast-reaction lim-its of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary dif-ferential equation on unbounded domains. Here, we replace the terms of the form uxx in usual reaction-diffusion equation, which represent linear diffusion, by terms of form φ(u)xx, representing nonlinear diffusion. For appropriate initial data, in the fast-reaction limit k → ∞, spatial segregation results in the two components of the original systems each converge to the positive and negative points of a self-similar limit profile f(η), where η = √xt , that satisfies one of four ordinary differential systems. The existence of these self-similar solutions of the k → ∞ limit problems is proved by using shooting methods which focus on a, the position of the free boundary which separates the regions where the solution is positive and where it is negative, and γ, the derivative of −φ(f) at η = a. The position of the free boundary gives us intuition how one substance penetrates into the other, so for specific forms of nonlinear diffusion, the relationship between the given form of the nonlinear diffusion and the position of the free boundary is also studied.</abstract><type>E-Thesis</type><journal/><volume/><journalNumber/><paginationStart/><paginationEnd/><publisher/><placeOfPublication>Swansea</placeOfPublication><isbnPrint/><isbnElectronic/><issnPrint/><issnElectronic/><keywords>Nonlinear diffusion; Reaction diffusion problem; Fast reaction; Free boundary; Self-similar solution</keywords><publishedDay>29</publishedDay><publishedMonth>7</publishedMonth><publishedYear>2022</publishedYear><publishedDate>2022-07-29</publishedDate><doi>10.23889/SUthesis.60766</doi><url/><notes>ORCiD identifier: https://orcid.org/0000-0002-9765-1314</notes><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><supervisor>Crooks, Elaine ; Mercuri, Carlo</supervisor><degreelevel>Doctoral</degreelevel><degreename>Ph.D</degreename><apcterm/><funders/><projectreference/><lastEdited>2022-08-05T16:41:34.6879800</lastEdited><Created>2022-08-05T16:26:43.5715149</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>YINI</firstname><surname>DU</surname><order>1</order></author></authors><documents><document><filename>60766__24888__d2f295452d9d4f66ab553c2c096ebeea.pdf</filename><originalFilename>Du_Yini_PhD_Thesis_Final_Redacted_Signature.pdf</originalFilename><uploaded>2022-08-05T16:34:59.6957234</uploaded><type>Output</type><contentLength>1552277</contentLength><contentType>application/pdf</contentType><version>E-Thesis – open access</version><cronfaStatus>true</cronfaStatus><documentNotes>Copyright: The author, Yini Du, 2022.</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807> |
spelling |
2022-08-05T16:41:34.6879800 v2 60766 2022-08-05 Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion 2bfcd9725f897025ac9db0056fd3dc64 YINI DU YINI DU true false 2022-08-05 In this thesis, we present an approach to characterising fast-reaction lim-its of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary dif-ferential equation on unbounded domains. Here, we replace the terms of the form uxx in usual reaction-diffusion equation, which represent linear diffusion, by terms of form φ(u)xx, representing nonlinear diffusion. For appropriate initial data, in the fast-reaction limit k → ∞, spatial segregation results in the two components of the original systems each converge to the positive and negative points of a self-similar limit profile f(η), where η = √xt , that satisfies one of four ordinary differential systems. The existence of these self-similar solutions of the k → ∞ limit problems is proved by using shooting methods which focus on a, the position of the free boundary which separates the regions where the solution is positive and where it is negative, and γ, the derivative of −φ(f) at η = a. The position of the free boundary gives us intuition how one substance penetrates into the other, so for specific forms of nonlinear diffusion, the relationship between the given form of the nonlinear diffusion and the position of the free boundary is also studied. E-Thesis Swansea Nonlinear diffusion; Reaction diffusion problem; Fast reaction; Free boundary; Self-similar solution 29 7 2022 2022-07-29 10.23889/SUthesis.60766 ORCiD identifier: https://orcid.org/0000-0002-9765-1314 COLLEGE NANME COLLEGE CODE Swansea University Crooks, Elaine ; Mercuri, Carlo Doctoral Ph.D 2022-08-05T16:41:34.6879800 2022-08-05T16:26:43.5715149 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics YINI DU 1 60766__24888__d2f295452d9d4f66ab553c2c096ebeea.pdf Du_Yini_PhD_Thesis_Final_Redacted_Signature.pdf 2022-08-05T16:34:59.6957234 Output 1552277 application/pdf E-Thesis – open access true Copyright: The author, Yini Du, 2022. true eng |
title |
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion |
spellingShingle |
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion YINI DU |
title_short |
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion |
title_full |
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion |
title_fullStr |
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion |
title_full_unstemmed |
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion |
title_sort |
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion |
author_id_str_mv |
2bfcd9725f897025ac9db0056fd3dc64 |
author_id_fullname_str_mv |
2bfcd9725f897025ac9db0056fd3dc64_***_YINI DU |
author |
YINI DU |
author2 |
YINI DU |
format |
E-Thesis |
publishDate |
2022 |
institution |
Swansea University |
doi_str_mv |
10.23889/SUthesis.60766 |
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 |
In this thesis, we present an approach to characterising fast-reaction lim-its of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary dif-ferential equation on unbounded domains. Here, we replace the terms of the form uxx in usual reaction-diffusion equation, which represent linear diffusion, by terms of form φ(u)xx, representing nonlinear diffusion. For appropriate initial data, in the fast-reaction limit k → ∞, spatial segregation results in the two components of the original systems each converge to the positive and negative points of a self-similar limit profile f(η), where η = √xt , that satisfies one of four ordinary differential systems. The existence of these self-similar solutions of the k → ∞ limit problems is proved by using shooting methods which focus on a, the position of the free boundary which separates the regions where the solution is positive and where it is negative, and γ, the derivative of −φ(f) at η = a. The position of the free boundary gives us intuition how one substance penetrates into the other, so for specific forms of nonlinear diffusion, the relationship between the given form of the nonlinear diffusion and the position of the free boundary is also studied. |
published_date |
2022-07-29T04:19:09Z |
_version_ |
1763754271740788736 |
score |
11.021648 |