Special Issue "Applications of Partial Differential Equations in Mathematical Physics"

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

Deadline for manuscript submissions: 31 March 2022.

Special Issue Editor

Prof. Dr. Panayiotis Vafeas
E-Mail Website
Guest Editor
Department of Chemical Engineering, University of Patras, University Campus, 26504 Patras, Greece
Interests: applied mathematics and mathematical physics; partial differential equations and applications in physical science and engineering; mathematical modelling and boundary value problems

Special Issue Information

Dear Colleagues,

Partial differential equations in mathematical physics provide a suitable platform for the development of original research in the fields of applied mathematics and physical sciences for the solution of boundary value problems with the introduction of partial differential equations and related methodologies. The purpose of this Special Issue is to gather contributions from experts on analytical and semi-analytical techniques with application domains, including but not limited to fluid dynamics, creeping hydrodynamics and magnetic fluids, direct and inverse scattering problems in wave phenomena, electromagnetism and low-frequency scattering, electric and magnetic activity of the brain, scattering of elastic waves from isotropic and anisotropic materials, mathematical modelling of cancer tumour growth, interaction with cold atmospheric pressure plasma jet systems and actuators, etc. Contributions with a main emphasis on numerical methods for the application of partial differential equations in mathematical physics are also welcome, provided they exploit analytical means at certain stages of the procedures employed for the derivations of the solutions.

Prof. Dr. Panayiotis Vafeas
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 papers will be 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 1600 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

  • mathematical physics
  • partial differential equations
  • boundary value problems
  • applications in science and engineering

Published Papers (1 paper)

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Research

Article
Interior Elastic Scattering by a Non-Penetrable Partially Coated Obstacle and Its Shape Recovering
Mathematics 2021, 9(19), 2485; https://doi.org/10.3390/math9192485 - 04 Oct 2021
Viewed by 309
Abstract
In this paper, the interior elastic direct and inverse scattering problem of time-harmonic waves for a non-penetrable partially coated obstacle placed in a homogeneous and isotropic medium is studied. The scattering problem is formulated via the Navier equation, considering incident circular waves due [...] Read more.
In this paper, the interior elastic direct and inverse scattering problem of time-harmonic waves for a non-penetrable partially coated obstacle placed in a homogeneous and isotropic medium is studied. The scattering problem is formulated via the Navier equation, considering incident circular waves due to point-source fields, where the corresponding scattered data are measured on a closed curve inside the obstacle. Our model, from the mathematical point of view, is described by a mixed boundary value problem in which the scattered field satisfies mixed Dirichlet-Robin boundary conditions on the Lipschitz boundary of the obstacle. Using a variational equation method in an appropriate Sobolev space setting, uniqueness and existence results as well as stability ones are established. The corresponding inverse problem is also studied, and using some specific auxiliary integral operators an appropriate modified factorisation method is given. In addition, an inversion algorithm for shape recovering of the partially coated obstacle is presented and proved. Last but not least, useful remarks and conclusions concerning the direct scattering problem and its linchpin with the corresponding inverse one are given. Full article
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