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Symmetry
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Symmetries in Evolution Equations and Applications
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Symmetries in Evolution Equations and Applications

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

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 7393

Special Issue Editors

Dr. Calogero Vetro

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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
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Dariusz Wardowski

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Guest Editor
Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland
Interests: fixed point theory; nonlinear analysis; differential equations
Prof. Dr. Bessem Samet

E-Mail Website
Guest Editor
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Interests: fixed point
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear colleagues,

Equations focusing on time-dependent systems play a relevant role in understanding and modelling various physical phenomena. In particular, we mention problems of heat transport and laser propagation in inhomogeneous media. The potential topics range from abstract theories to concrete applications. We aim to deeply discuss the qualitative behavior of the equations. The existence and absence of local and global solutions, the asymptotic analysis of solutions, and the occurrence of blow ups are some of the crucial questions to deal with. Symmetry methods of evolution equations play a crucial role in this investigation: conditions constraining the equation on its Lie and (contact-)point symmetries help in the classification of evolution equations possessing nonlocal symmetries; potential symmetries establishing the equivalence between two different evolution equations originate methods for obtaining new from already known solutions; and algebraic structures of symmetries are useful in studying physical systems and developing admissible transformations among them.

This Special Issue aims to collect original and significant contributions dealing with both the theory and applications of evolution equations and their systems. This Special Issue also seeks to serve as a platform for the exchange of ideas between scientists of different disciplines interested in evolution equations and their applications.

Dr. Calogero Vetro
Prof. Dr. Dariusz Wardowski
Prof. Dr. Bessem Samet
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

  • complex symmetry
  • critical exponents
  • Lie symmetries
  • local and global solutions
  • reduction methods

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Published Papers (4 papers)

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Research

17 pages, 335 KiB  
Article
A One-Dimensional Time-Fractional Damped Wave Equation with a Convection Term
by Ibtisam Aldawish, Mohamed Jleli and Bessem Samet
Symmetry 2023, 15(5), 1071; https://doi.org/10.3390/sym15051071 - 12 May 2023
Viewed by 935
Abstract
We investigate a semilinear time-fractional damped wave equation in one dimension, posed in a bounded interval. The considered equation involves a convection term and singular potentials on one extremity of the interval. A Dirichlet boundary condition depending on the time-variable is imposed. Using [...] Read more.
We investigate a semilinear time-fractional damped wave equation in one dimension, posed in a bounded interval. The considered equation involves a convection term and singular potentials on one extremity of the interval. A Dirichlet boundary condition depending on the time-variable is imposed. Using nonlinear capacity estimates, we establish sufficient conditions for the nonexistence of weak solutions to the considered problem. In particular, when the boundary condition is independent of time, we show the existence of a Fujita-type critical exponent. Full article
(This article belongs to the Special Issue Symmetries in Evolution Equations and Applications)
12 pages, 287 KiB  
Article
An Improved Regularity Criterion for the 3D Magnetic Bénard System in Besov Spaces
by Muhammad Naqeeb, Amjad Hussain and Ahmad M. Alghamdi
Symmetry 2022, 14(9), 1918; https://doi.org/10.3390/sym14091918 - 13 Sep 2022
Cited by 3 | Viewed by 1318
Abstract
This article notably targets the more general (extended) function spaces by investigating the regularity of the weak solutions or turbulent solutions to the Cauchy problem of the 3D magnetic Bénard system by converting it into mathematical symmetric form, in the absence of thermal [...] Read more.
This article notably targets the more general (extended) function spaces by investigating the regularity of the weak solutions or turbulent solutions to the Cauchy problem of the 3D magnetic Bénard system by converting it into mathematical symmetric form, in the absence of thermal diffusion, in terms of pressure. In that regard, we successfully improved the results by obtaining sufficient integrable regularity conditions for the pressure and gradient pressure in the homogeneous Besov spaces. Full article
(This article belongs to the Special Issue Symmetries in Evolution Equations and Applications)
16 pages, 314 KiB  
Article
Optimal Control for a Class of Riemann-Liouville Fractional Evolution Inclusions
by He Yang and Qian Ren
Symmetry 2022, 14(2), 248; https://doi.org/10.3390/sym14020248 - 27 Jan 2022
Cited by 1 | Viewed by 1825
Abstract
In this paper, under symmetric properties of multivalued operators, the existence of mild solutions as well as optimal control for the nonlocal problem of fractional semilinear evolution inclusions are investigated in abstract spaces. At first, the existence results are proved by applying the [...] Read more.
In this paper, under symmetric properties of multivalued operators, the existence of mild solutions as well as optimal control for the nonlocal problem of fractional semilinear evolution inclusions are investigated in abstract spaces. At first, the existence results are proved by applying the theory of operator semigroups and the fixed-point theorem of multivalued mapping. Then the existence theorem on the optimal state-control pair is proved by constructing the minimizing sequence twice. An example is given in the last section as an application of the obtained conclusions. Full article
(This article belongs to the Special Issue Symmetries in Evolution Equations and Applications)
9 pages, 257 KiB  
Article
Cubic–Quartic Optical Soliton Perturbation with Differential Group Delay for the Lakshmanan–Porsezian–Daniel Model by Lie Symmetry
by Sachin Kumar, Anjan Biswas, Yakup Yıldırım, Luminita Moraru, Simona Moldovanu, Hashim M. Alshehri, Dalal Adnan Maturi and Dalal H. Al-Bogami
Symmetry 2022, 14(2), 224; https://doi.org/10.3390/sym14020224 - 24 Jan 2022
Cited by 8 | Viewed by 2267
Abstract
This paper employs Lie symmetry analysis to recover cubic–quartic optical soliton solutions to the Lakshmanan–Porsezian–Daniel model in birefringent fibers. The results are a sequel to the previously reported work on the same model in unpolarized fibers. Dark, singular, and straddled optical solitons that [...] Read more.
This paper employs Lie symmetry analysis to recover cubic–quartic optical soliton solutions to the Lakshmanan–Porsezian–Daniel model in birefringent fibers. The results are a sequel to the previously reported work on the same model in unpolarized fibers. Dark, singular, and straddled optical solitons that emerged from the scheme are presented. Full article
(This article belongs to the Special Issue Symmetries in Evolution Equations and Applications)
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