Applications of Differential Equations in Sciences

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 30 November 2024 | Viewed by 1176

Special Issue Editors


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Guest Editor
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria
Interests: cellular neural networks; differential equations; modeling; numerical methods
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
1. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria
2. Climate, Atmosphere and Water Research Institute, Bulgarian Academy of Sciences, Blvd., Tzarigradsko Chaussee 66, 1784 Sofia, Bulgaria
Interests: nonlinear dynamics; nonlinear time series analysis; fluid mechanics; nonlinear partial differential equations; application of the methods of statistics and probability theory to natural, social and economic systems
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, Sofia 1113, Bulgaria
Interests: mathematical modeling; theory of dynamical systems; theory of non-linear waves

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to many applications of differential equations in different fields of science. Several phenomena in nature (physics, chemistry, and biology) and society (economics) result in problems leading to the study of linear and nonlinear differential equations.

It is known that many natural phenomena are not static, but depend both on the instantaneous values of given quantities and the type of their change. Such phenomena must be described mathematically with differential equations and the mathematical models built with their help. In this way, many of the fundamental laws of physics and chemistry are defined, and in biology and economics, differential equations model the behavior of systems of great complexity. In many cases, completely different problems from unrelated scientific fields can be reduced to the same differential equations. For example, the propagation of light and sound in air and of waves on a water surface can be described by the same partial differential equation: the wave equation. Heat transfer, the theory developed by Joseph Fourier at the beginning of the 19th century, is described by another partial differential equation of the second order: heat conduction. Subsequently, it turns out that many other processes can be described with the same or similar equations, such as Brownian motion (Fokker–Planck equation) or the behavior of financial markets in the Black–Scholes model.

The main topics of this Special Issue are:

  • Applications in mathematical physics;
  • Applications in mechanics;
  • Applications in fractional calculus;
  • Applications in financial mathematics;
  • Applications in mathematical biology;
  • Applications in numerical methods and computer science.

Prof. Dr. Angela Slavova
Prof. Dr. Nikolay K. Vitanov
Prof. Dr. Elena V. Nikolova
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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
  • mathematical physics
  • mechanics
  • financial mathematics
  • fractional calculus
  • mathematical biology
  • numerical methods
  • neuroscience

Published Papers (2 papers)

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Research

14 pages, 300 KiB  
Article
Spatial Decay Estimates and Continuous Dependence for the Oldroyd Fluid
by Yuanfei Li
Mathematics 2024, 12(8), 1240; https://doi.org/10.3390/math12081240 - 19 Apr 2024
Viewed by 401
Abstract
This article investigates the Oldroyd fluid, which is widely used in industrial and engineering environments. When the Oldroyd fluid passes through a three-dimensional semi-infinite cylinder, the asymptotic properties of the solutions are established. On this basis, we also studied the continuous dependence of [...] Read more.
This article investigates the Oldroyd fluid, which is widely used in industrial and engineering environments. When the Oldroyd fluid passes through a three-dimensional semi-infinite cylinder, the asymptotic properties of the solutions are established. On this basis, we also studied the continuous dependence of the viscosity coefficient. Full article
(This article belongs to the Special Issue Applications of Differential Equations in Sciences)
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24 pages, 375 KiB  
Article
Some Non-Linear Evolution Equations and Their Explicit Smooth Solutions with Exponential Growth Written into Integral Form
by Petar Popivanov and Angela Slavova
Mathematics 2024, 12(7), 1003; https://doi.org/10.3390/math12071003 - 27 Mar 2024
Viewed by 560
Abstract
In this paper, exact solutions of semilinear equations having exponential growth in the space variable x are found. Semilinear Schrödinger equation with logarithmic nonlinearity and third-order evolution equations arising in optics with logarithmic and power-logarithmic nonlinearities are investigated. In the parabolic case, the [...] Read more.
In this paper, exact solutions of semilinear equations having exponential growth in the space variable x are found. Semilinear Schrödinger equation with logarithmic nonlinearity and third-order evolution equations arising in optics with logarithmic and power-logarithmic nonlinearities are investigated. In the parabolic case, the solution u is written as u=beax2, a<0, a,b being real-valued functions. We are looking for the solutions u of Schrödinger-type equation of the form u=beax22, respectively, for the third-order PDE, u=AeiΦ, where the amplitude b and the phase function a are complex-valued functions, A>0, and Φ is real-valued. In our proofs, the method of the first integral is used, not Hirota’s approach or the method of simplest equation. Full article
(This article belongs to the Special Issue Applications of Differential Equations in Sciences)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

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