Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
2.0
Journals
Axioms
Special Issues
Advances in Reaction Diffusion Systems and Applications
share announcement

Advances in Reaction Diffusion Systems and Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (10 June 2022) | Viewed by 3634

Special Issue Editor

Prof. Dr. Jeff Morgan

E-Mail Website
Guest Editor
Department of Mathematics, University of Houston, Houston, TX 77204-3308, USA
Interests: reaction-diffusion systems; mathematical biology

Special Issue Information

Dear Colleagues,

We have launched a Special Issue of Axioms that will present current perspectives regarding advances in reaction–diffusion systems and applications to address recent advances in the field related to theory that addresses well-posedness, global existence, asymptotic behavior, pattern formation, and applications to chemical, biological, population, disease, and other models of general interest. Reaction–diffusion systems have played a central role in mathematical modeling of a wide variety of phenomena in physics, biology, and other applied sciences. Their study is driven both by theoretical interest and their use in modeling real world problems. We hope to provide a platform to bring together experts as well as young researchers in the area to promote and share knowledge and to foster communication and applications. Research papers as well as review articles are welcome. 

Prof. Dr. Jeff Morgan
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Differential equations
  • Partial differential equations
  • Boundary conditions
  • Mass transport boundary conditions
  • Dynamic boundary conditions
  • Diffusion
  • Convection
  • Reaction vector field
  • Well-posedness
  • Global existence
  • Asymptotic behavior
  • Pattern formation

Published Papers (2 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

16 pages, 353 KiB  
Article
Global Existence for Reaction-Diffusion Systems on Multiple Domains
by William E. Fitzgibbon, Jeff Morgan and John Ryan
Axioms 2022, 11(7), 335; https://doi.org/10.3390/axioms11070335 - 11 Jul 2022
Cited by 1 | Viewed by 1267
Abstract
In this work, we study the global existence of solutions reaction-diffusion systems with control of mass on multiple domains. Some of these domains overlap, and as a result, an unknown defined on one subdomain can impact another unknown defined on a different domain [...] Read more.
In this work, we study the global existence of solutions reaction-diffusion systems with control of mass on multiple domains. Some of these domains overlap, and as a result, an unknown defined on one subdomain can impact another unknown defined on a different domain that intersects with the first. The question addressed is related to the long standing question of global existence for reaction-diffusion systems with quasi-positive reaction vector fields that dissipate mass, in the setting of a single bounded spatial domain. The results extend recent work of the authors and others for systems on a single domain with L∞ diffusion and quasi-positive reaction vector fields that dissipate mass, in the setting of multiple domains. Full article
(This article belongs to the Special Issue Advances in Reaction Diffusion Systems and Applications)
►▼ Show Figures

Figure 1

13 pages, 1511 KiB  
Article
On Large and Small Data Blow-Up Solutions in the Trojan Y Chromosome Model
by Eric M. Takyi, Matthew A. Beauregard, Thomas Griffin, Landrey Bobo and Rana D. Parshad
Axioms 2022, 11(3), 120; https://doi.org/10.3390/axioms11030120 - 09 Mar 2022
Cited by 2 | Viewed by 1703
Abstract
The Trojan Y Chromosome Strategy (TYC) is the only genetic biological control method in practice in North America for controlling invasive populations with an XX–XY sex determinism. Herein a modified organism, that is a supermale or feminised supermale, is introduced into an invasive [...] Read more.
The Trojan Y Chromosome Strategy (TYC) is the only genetic biological control method in practice in North America for controlling invasive populations with an XX–XY sex determinism. Herein a modified organism, that is a supermale or feminised supermale, is introduced into an invasive population to skew the sex ratio over time, causing local extinction. We consider the three species TYC reaction diffusion model, and show that introduction of supermales above certain thresholds, and for certain initial data, solutions can blow-up in finite time. Thus, in order to have biologically meaningful solutions, one needs to restrict parameter and initial data regimes, in TYC type models. Full article
(This article belongs to the Special Issue Advances in Reaction Diffusion Systems and Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-2
Back to TopTop