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Symmetry
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Symmetry and Partial Differential Equations: Theory and Application
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Symmetry and Partial Differential Equations: Theory and Application

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

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 5743

Special Issue Editor

Dr. Hu Chen

E-Mail Website
Guest Editor
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
Interests: fractional calculus; numerical analysis; numerical approximation for partial differential equations; spectral methods

Special Issue Information

Dear Colleagues,

Partial differential equations are widely used for modelling in physics, mechanics, chemistry and other natural sciences. Studying solution properties using partial differential equations is very useful for understanding natural phenomena. In this Special Issue, we aim to present the latest research on the solution theory and applications of the partial differential equations. In particularly, we are also interested in articles on the numerical approximation of partial differential equations (finite difference methods, finite element methods, spectral methods and other numerical methods are welcome) and inverse problems of partial differential equations, including fractional partial differential equations (time fractional, space fractional and space–time fractional PDEs are all welcome).

Dr. Hu Chen
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

  • symmetries
  • partial differential equations
  • numerical analysis
  • numerical solution
  • fractional calculus
  • time fractional PDEs

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Published Papers (3 papers)

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Research

25 pages, 359 KiB  
Article
Weakly Coupled Systems of Semi-Linear Fractional σ–Evolution Equations with Different Power Nonlinearities
by Seyyid Ali Saiah, Abdelatif Kainane Mezadek, Mohamed Kainane Mezadek, Abdelhamid Mohammed Djaouti, Ashraf Al-Quran and Ali M. A. Bany Awad
Symmetry 2024, 16(7), 884; https://doi.org/10.3390/sym16070884 - 11 Jul 2024
Viewed by 511
Abstract
The study of small data Sobolev solutions to the Cauchy problem for weakly coupled systems of semi-linear fractional σ–evolution equations with different power nonlinearities is of interest to us in this research. These solutions must exist globally (in time). We explain [...] Read more.
The study of small data Sobolev solutions to the Cauchy problem for weakly coupled systems of semi-linear fractional σ–evolution equations with different power nonlinearities is of interest to us in this research. These solutions must exist globally (in time). We explain the relationships between the admissible range of exponents p1 and p2 symmetrically in our main modeland the regularity assumptions for the data by using Lm−Lq estimates of Sobolev solutions to related linear models with a vanishing right-hand side and some fixed point argument. This allows us to prove the global (in time) existence of small data Sobolev solutions. Full article
(This article belongs to the Special Issue Symmetry and Partial Differential Equations: Theory and Application)
21 pages, 849 KiB  
Article
A Comparative Study of the Fractional Partial Differential Equations via Novel Transform
by Abdul Hamid Ganie, Mashael M. AlBaidani and Adnan Khan
Symmetry 2023, 15(5), 1101; https://doi.org/10.3390/sym15051101 - 17 May 2023
Cited by 16 | Viewed by 2257
Abstract
In comparison to fractional-order differential equations, integer-order differential equations generally fail to properly explain a variety of phenomena in numerous branches of science and engineering. This article implements efficient analytical techniques within the Caputo operator to investigate the solutions of some fractional partial [...] Read more.
In comparison to fractional-order differential equations, integer-order differential equations generally fail to properly explain a variety of phenomena in numerous branches of science and engineering. This article implements efficient analytical techniques within the Caputo operator to investigate the solutions of some fractional partial differential equations. The Adomian decomposition method, homotopy perturbation method, and Elzaki transformation are used to calculate the results for the specified issues. In the current procedures, we first used the Elzaki transform to simplify the problems and then applied the decomposition and perturbation methods to obtain comprehensive results for the problems. For each targeted problem, the generalized schemes of the suggested methods are derived under the influence of each fractional derivative operator. The current approaches give a series-form solution with easily computable components and a higher rate of convergence to the precise solution of the targeted problems. It is observed that the derived solutions have a strong connection to the actual solutions of each problem as the number of terms in the series solution of the problems increases. Graphs in two and three dimensions are used to plot the solution of the proposed fractional models. The methods used currently are simple and efficient for dealing with fractional-order problems. The primary benefit of the suggested methods is less computational time. The results of the current study will be regarded as a helpful tool for dealing with the solution of fractional partial differential equations. Full article
(This article belongs to the Special Issue Symmetry and Partial Differential Equations: Theory and Application)
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23 pages, 5285 KiB  
Article
Negative Poisson’s Ratio Re-Entrant Base Modeling and Vibration Isolation Performance Analysis
by Kun Pan, Wei Zhang and Jieyu Ding
Symmetry 2022, 14(7), 1356; https://doi.org/10.3390/sym14071356 - 30 Jun 2022
Cited by 2 | Viewed by 1846
Abstract
Negative Poisson’s ratio materials are increasingly used in the design of vibration isolation bases due to their unique tensile properties. In this paper, based on the expansion feature of the negative Poisson’s ratio re-entrant structure, the influence of the size of the re-entrant [...] Read more.
Negative Poisson’s ratio materials are increasingly used in the design of vibration isolation bases due to their unique tensile properties. In this paper, based on the expansion feature of the negative Poisson’s ratio re-entrant structure, the influence of the size of the re-entrant structure within a single structure was analyzed, and a honeycomb base was designed with a negative Poisson’s ratio re-entrant structure. A new modeling method for the honeycomb base is proposed. In the modeling process, the honeycomb base was analyzed according to its symmetry using the Lagrange equation for base modeling and the finite element consistent mass matrix was introduced to simplify the calculation. The vibration isolation performance of the honeycomb base was evaluated by vibration level difference. COMSOL software was used to simulate and analyze the cellular base in order to verify the correctness of the results obtained from numerical modeling. In conclusion, the honeycomb base had a vibration isolation effect on external excitation in the vertical direction of the base. Furthermore, the vibration isolation performance of the base was greatly related to the wall thickness and Poisson’s ratio of the re-entrant structure. Full article
(This article belongs to the Special Issue Symmetry and Partial Differential Equations: Theory and Application)
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