Differential Equations of Mathematical Physics and Related Problems of Mechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Functional Interpolation".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 11188

Special Issue Editors

1. Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia
2. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Interests: partial differential equations & mathematical physics; elasticity system; stokes system; biharmonic (polyharmonic) equation
Special Issues, Collections and Topics in MDPI journals
Department of General Mathematics, Lomonosov Moscow State University, Moscow 11992, Russia
Interests: quasi-classical asymtotics of ODE’s and PDE’s; resurgent analysis; functional analysis
Special Issues, Collections and Topics in MDPI journals
1. Institute of Applied Mechanics, Russian Academy of Sciences, Moscow 125040, Russia
2. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow 119526, Russia
3. Lomonosov Moscow State University, Moscow 11992, Russia
4. Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow 119333, Russia
Interests: continuum mechanics; gradient theory; micropolar and micro-morphic models

Special Issue Information

Dear Colleagues,

The main topics of this Special Issue are:

  • Mathematical Physics and PDE

Asymtotics of ODEs and PDEs; mathematical physics and PDE including fluid dynamics, wave equation, Boltzmann equation; solvability, regularity, stability and other qualitative properties of linear and nonlinear equations and systems; spectral theory, scattering, inverse problems; variational methods and calculus of variations; fluid dynamics; dynamical systems;

  • Applied Mathematics

Numerical methods of ODEs and PDEs, nonlinear problems, bifurcations, stability, chaos and fractals, fractional calculus;

  • Related Problems of Analysis and Continuum Mechanics

Stochastic models and probabilistic methods including random matrices and stochastic PDE; variational formulations of gradient elasticity theories, micropolar and micromorphic models of solids and fluids; constructive methods for representing solutions in the high-order theories of solids; general representations of solutions; nonlocal effects (interactions) and smooth solutions for bodies with nonsmooth geometry; identification of materials parameters of generalized continuum theories; size-dependent models of thin structures and composite materials; nonclassical dynamic effects in generalized media; gradient theories in multiphysics, including thermodynamic, thermodiffusion, electroelasticity processes in the nano- and microfields of mechanical engineering and related applied problems.

Prof. Dr. Hovik Matevossian
Prof. Dr. Maria Korovina
Prof. Dr. Sergey Lurie
Guest Editors

Manuscript Submission Information

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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.

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Published Papers (10 papers)

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Editorial

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5 pages, 159 KiB  
Editorial
“Differential Equations of Mathematical Physics and Related Problems of Mechanics”—Editorial 2021–2023
Mathematics 2024, 12(1), 150; https://doi.org/10.3390/math12010150 - 02 Jan 2024
Viewed by 462
Abstract
Based on the published papers in this Special Issue of the elite scientific journal Mathematics, we herein present the Editorial for “Differential Equations of Mathematical Physics and Related Problems of Mechanics”, the main topics of which are fundamental and applied research on [...] Read more.
Based on the published papers in this Special Issue of the elite scientific journal Mathematics, we herein present the Editorial for “Differential Equations of Mathematical Physics and Related Problems of Mechanics”, the main topics of which are fundamental and applied research on differential equations in mathematical physics and mechanics [...] Full article

Research

Jump to: Editorial

12 pages, 430 KiB  
Article
Analytical Solutions of Partial Differential Equations Modeling the Mechanical Behavior of Non-Prismatic Slender Continua
Mathematics 2023, 11(23), 4723; https://doi.org/10.3390/math11234723 - 22 Nov 2023
Viewed by 505
Abstract
Non-prismatic slender continua are the prototypical models of many structural elements used in engineering applications, such as wind turbine blades and towers. Unfortunately, closed-form expressions for stresses and strains in such continua are much more difficult to find than in prismatic ones, e.g., [...] Read more.
Non-prismatic slender continua are the prototypical models of many structural elements used in engineering applications, such as wind turbine blades and towers. Unfortunately, closed-form expressions for stresses and strains in such continua are much more difficult to find than in prismatic ones, e.g., the de Saint-Venant’s cylinder, for which some analytical solutions are known. Starting from a suitable mechanical model of a tapered slender continuum with one dimension much larger than the other tapered two, a variational principle is exploited to derive the field equations, i.e., the set of partial differential equations and boundary conditions that govern its state of stress and strain. The obtained equations can be solved in closed form only in a few cases. Paradigmatic examples in which analytical solutions are obtainable in terms of stresses, strains, or related mechanical quantities of interest in engineering applications are presented and discussed. Full article
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