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Symmetry
Special Issues
Symmetry and Biomathematics: Recent Developments and Challenges
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Symmetry and Biomathematics: Recent Developments and Challenges

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (17 February 2023) | Viewed by 7204

Special Issue Editors

Prof. Dr. Wenjun Liu

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
Interests: partial differential equations; asymptotic analysis; nonlinear waves; mathematical physics; soliton theory; nonlinear analysis; biomedicine; biomathematics
Prof. Dr. Mariano Torrisi

E-Mail Website
Guest Editor
Dipartimento di Matematica e Informatica, University of Catania, Catania, Italy
Interests: group methods for nonlinear differential equations (both ODEs and PDEs); reduction techniques for the search of exact solutions of PDEs; applications of the group methods to reaction diffusion models, such as nonlinear governing equations modeling population dynamics and biomathematical problems; nonlinear diffusion and propagation of heat
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Roman M. Cherniha

E-Mail Website
Guest Editor
Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine
Interests: non-linear pdes: lie and conditional symmetries, exact solutions and their properties; application of symmetry-based methods for analytical solving nonlinear initial and boundary value problems arising in mathematical physics and mathematical biology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry and asymmetry have always been ubiquitous in nature, especially in the origin of life, biological evolution and the process of disease, which has attracted extensive attention of biologists, biomathematics and biomedical researchers.

The law of motion of matter can be studied from the angle of symmetry transformation and symmetry operation. Therefore, it is very enlightening to start from group theory. It is of great significance to search for the symmetries that occur in the laws of biology, to study the symmetries that occur in biological systems at the molecular and macro level, and to discuss the process of the symmetries that gradually break down in the course of disease development.

The aim of the present Special Issue is to emphasize the recent developments and challenges in symmetry and biomathematics. For example, we focus on the latest research on symmetry and travelling wave analysis, on transformations for models in biomathematics, on symmetry for disease models (especially related to the COVID-19 pandemic), on symmetry in neuroscience, and on pulse propagation in biological systems. Symmetry analysis of stochastic real-world  models and models based on nonlinear reaction-diffusion equations are also what we are interested in.

We are soliciting contributions (research and review articles) covering a broad range of topics on all the above-mentioned topics.

Prof. Dr. Wenjun Liu
Prof. Dr. Mariano Torrisi
Prof. Dr. Roman M. Cherniha
Guest Editors

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. Symmetry 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

  • travelling wave analysis
  • lie symmetry
  • conditional and nonclassical symmetry
  • exact solutions of nonlinear PDEs
  • transformations for models in biomathematics
  • evolution of disease models
  • development of population models
  • symmetry analysis of stochastic models
  • pulse propagation in biological systems
  • symmetry in neuroscience
  • stability and instability of biological systems

Published Papers (5 papers)

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Research

10 pages, 260 KiB  
Article
Symmetries and Solutions for Some Classes of Advective Reaction–Diffusion Systems
by Mariano Torrisi and Rita Tracinà
Symmetry 2022, 14(10), 2009; https://doi.org/10.3390/sym14102009 - 25 Sep 2022
Cited by 3 | Viewed by 1149
Abstract
In this paper, we consider some reaction–advection–diffusion systems in order to obtain exact solutions via a symmetry approach. We write the determining system of a general class. Then, for particular subclasses, we obtain special forms of the arbitrary constitutive parameters that allow us [...] Read more.
In this paper, we consider some reaction–advection–diffusion systems in order to obtain exact solutions via a symmetry approach. We write the determining system of a general class. Then, for particular subclasses, we obtain special forms of the arbitrary constitutive parameters that allow us to extend the principal Lie algebra. In some cases, we write the corresponding reduced system and we find special exact solutions. Full article
(This article belongs to the Special Issue Symmetry and Biomathematics: Recent Developments and Challenges)
17 pages, 324 KiB  
Article
Analysis of Solutions to a Free Boundary Problem with a Nonlinear Gradient Absorption
by Haihua Lu, Shu Xie and Yujuan Chen
Symmetry 2022, 14(8), 1619; https://doi.org/10.3390/sym14081619 - 06 Aug 2022
Viewed by 1156
Abstract
In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption and the free boundary. By using the comparison principle and super-sub solution method, we obtain some sufficient conditions on the global existence, blow-up in [...] Read more.
In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption and the free boundary. By using the comparison principle and super-sub solution method, we obtain some sufficient conditions on the global existence, blow-up in finite time of solutions, and blow-up sets when blow-up phenomenon occurs. Furthermore, the global solution is bounded and uniformly tends to zero, and it is either a global fast solution or a global slow solution. Finally, we obtain a trichotomy conclusion by considering the size of parameter σ. Full article
(This article belongs to the Special Issue Symmetry and Biomathematics: Recent Developments and Challenges)
13 pages, 306 KiB  
Article
Analysis of Solutions to a Parabolic System with Absorption
by Haihua Lu, Jiayuan Wu and Wenjun Liu
Symmetry 2022, 14(6), 1274; https://doi.org/10.3390/sym14061274 - 20 Jun 2022
Cited by 2 | Viewed by 1109
Abstract
In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption under the homogeneous Dirichlet boundary. By using the comparison principle and super-sub solution method, we obtain some sufficient conditions for the global existence and [...] Read more.
In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption under the homogeneous Dirichlet boundary. By using the comparison principle and super-sub solution method, we obtain some sufficient conditions for the global existence and blow-up in finite time of solutions and establish some estimates of the upper and lower bounds of the blow-up rates. For the special case, if the domain is symmetric, for example, if it is a ball, the results of this paper also hold. Full article
(This article belongs to the Special Issue Symmetry and Biomathematics: Recent Developments and Challenges)
18 pages, 1064 KiB  
Article
First-Order Sign-Invariants and Exact Solutions of the Radially Symmetric Nonlinear Diffusion Equations with Gradient-Dependent Diffusivities
by Lina Ji, Xiankang Luo, Jiao Zeng, Min Xiao and Yuanhua Meng
Symmetry 2022, 14(2), 386; https://doi.org/10.3390/sym14020386 - 15 Feb 2022
Viewed by 1284
Abstract
The sign-invariant theory is used to study the radially symmetric nonlinear diffusion equations with gradient-dependent diffusivities. The first-order non-stationary sign-invariants and the first-order non-autonomous sign-invariants admitted by the governing equations are identified. As a consequence, the exact solutions to the resulting equations are [...] Read more.
The sign-invariant theory is used to study the radially symmetric nonlinear diffusion equations with gradient-dependent diffusivities. The first-order non-stationary sign-invariants and the first-order non-autonomous sign-invariants admitted by the governing equations are identified. As a consequence, the exact solutions to the resulting equations are constructed due to the corresponding reductions. The phenomena of blow-up, extinction and behavior of some solutions are also described. Full article
(This article belongs to the Special Issue Symmetry and Biomathematics: Recent Developments and Challenges)
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11 pages, 265 KiB  
Article
Lie Symmetries and Solutions of Reaction Diffusion Systems Arising in Biomathematics
by Mariano Torrisi and Rita Traciná
Symmetry 2021, 13(8), 1530; https://doi.org/10.3390/sym13081530 - 20 Aug 2021
Cited by 8 | Viewed by 1834
Abstract
In this paper, a special subclass of reaction diffusion systems with two arbitrary constitutive functions Γ(v) and H(u,v) is considered in the framework of transformation groups. These systems arise, quite often, as mathematical models, in [...] Read more.
In this paper, a special subclass of reaction diffusion systems with two arbitrary constitutive functions Γ(v) and H(u,v) is considered in the framework of transformation groups. These systems arise, quite often, as mathematical models, in several biological problems and in population dynamics. By using weak equivalence transformation the principal Lie algebra, LP, is written and the classifying equations obtained. Then the extensions of LP are derived and classified with respect to Γ(v) and H(u,v). Some wide special classes of special solutions are carried out. Full article
(This article belongs to the Special Issue Symmetry and Biomathematics: Recent Developments and Challenges)
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