Symmetry in Ordinary and Partial Differential Equations and Applications II

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

Deadline for manuscript submissions: 15 April 2024 | Viewed by 1665

Special Issue Editor


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Guest Editor
Associate Professor, Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy
Interests: difference equations; flow invariance; nonlinear regularity theory; ordinary differential equations; partial differential equations; reduction methods; symmetry operators; weak symmetries
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Special Issue Information

Dear Colleagues,

Due to the great success of our Special Issue "Symmetry in Ordinary and Partial Differential Equations and Applications" we decided to set up a second volume. 

Ordinary and partial differential equations are universally recognized as powerful tools to model and solve practical problems involving nonlinear phenomena. In particular, we mention physical processes as problems in elasticity theory, where we deal with composites made of two different materials with different hardening exponents.

Therefore, the theory of differential equations has been successfully applied to establish the existence and multiplicity of solutions of boundary value problems via direct methods, minimax theorems, variational methods, and topological methods. If possible, one looks to solutions in special forms by using the symmetries of the driving equation. This also leads to the study of the difference counterparts of such equations to provide exact or approximate solutions. We mention the reduction methods for establishing exact solutions as solutions of lower-dimensional equations. The methods of symmetrization are a key tool in obtaining a priori estimates of solutions to various classes of differential equations, provided that both the involved functions and the data of the problem admit some partial or fully symmetries on the framework space. In particular, comparison principles and method of moving planes up to a critical position, deserve further investigation to prove spherical or axial symmetry results for positive solutions.

This Special Issue aims to collect original and significant contributions dealing with both the theory and applications of differential equations. Also, this Special Issue may serve as a platform for the exchange of ideas between scientists of different disciplines interested in ordinary and partial differential equations and their applications.

Welcome to read the publications in "Symmetry in Ordinary and Partial Differential Equations and Applications" at https://www.mdpi.com/journal/symmetry/topical_collections/Symmetry_Ordinary_Partial_Differential_Equations_Applications.

Dr. Calogero Vetro
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. 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

  • difference equations
  • flow invariance
  • nonlinear regularity theory
  • ordinary differential equations
  • partial differential equations
  • reduction methods
  • symmetry operators
  • weak symmetries

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Published Papers (1 paper)

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Research

33 pages, 3560 KiB  
Article
Computational Modeling of Individual Red Blood Cell Dynamics Using Discrete Flow Composition and Adaptive Time-Stepping Strategies
by Aymen Laadhari and Ahmad Deeb
Symmetry 2023, 15(6), 1138; https://doi.org/10.3390/sym15061138 - 24 May 2023
Cited by 1 | Viewed by 1361
Abstract
In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in a non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to the Canham–Helfrich model and maintains [...] Read more.
In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in a non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to the Canham–Helfrich model and maintains surface inextensibility constraint through penalty. We propose a two-step time integration scheme that incorporates higher-order accuracy by using an asymmetric composition of discrete flow based on the second-order backward difference formula, followed by a projection onto the real axis. Our framework incorporates variable time steps generated by an appropriate adaptation criterion. We validate our model through numerical simulations against existing experimental and numerical results in the case of purely Newtonian flow. Furthermore, we provide preliminary results demonstrating the influence of the non-Newtonian fluid model on membrane regimes. Full article
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