Wave Scattering and Differential Equations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 20 December 2024 | Viewed by 904

Special Issue Editor


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Guest Editor
Department of Statistics and Insurance Science, School of Finance and Statistics, University of Piraeus, 18534 Piraeus, Greece
Interests: applied mathematics and mathematical physics; partial differential equations; stochastic partial differential equations; integral equations; boundary value problems; wave propagation and scattering of acoustic, electromagnetic and elastic waves—direct and inverse problems; mathematical modelling of wave problems and applications

Special Issue Information

Dear Colleagues,

This new Special Issue focuses on publishing original contributions concerning the theory of differential equations and their applications in the fields of applied mathematics and physical sciences. Papers regarding new theoretical and numerical techniques, novel ideas, and new analysis tools are suitable topics for the Special Issue. The research articles we wish to publish will be addressed not only to mathematicians but also to a wider array of scientists, such as engineers and physical scientists, for whom differential equations are valuable and make up their main mathematical tools.

Research areas include ordinary and partial differential equations, stochastic partial differential equations, and integral equations with application domains, including but not limited to boundary value problems, wave propagation and scattering, scattering of acoustic, electromagnetic, and elastic waves, and the direct and inverse problems with linchpin to theoretical and numerical approaches to their solutions.

The readership of the Issue, except applied mathematicians, physical scientists, and engineers, also includes those working in radar, optics, geophysics, biology, acoustics, elasticity, communication theory, signal processing, and imaging science, among other sectors.

Prof. Dr. Vassilios Sevroglou
Guest Editor

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Keywords

  • partial differential equations
  • stochastic partial differential equations
  • integral equations
  • boundary value problems
  • wave scattering
  • mathematical modeling

Published Papers (1 paper)

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Research

17 pages, 382 KiB  
Article
Two-Dimensional Scattering of Line Source Electromagnetic Waves by a Layered Obstacle
by Christodoulos E. Athanasiadis and Paraskevi Roupa
Mathematics 2023, 11(19), 4119; https://doi.org/10.3390/math11194119 - 29 Sep 2023
Viewed by 596
Abstract
We consider the scattering problem of line source electromagnetic waves using a multi-layered obstacle with a core, which may be a perfect conductor, a dielectric, or has an impedance surface. We formulate this problem in two dimensions and we prove some useful scattering [...] Read more.
We consider the scattering problem of line source electromagnetic waves using a multi-layered obstacle with a core, which may be a perfect conductor, a dielectric, or has an impedance surface. We formulate this problem in two dimensions and we prove some useful scattering relations. In particular, we state and prove a reciprocity principle and a general scattering theorem for line source waves for any possible positions of the source. These theorems can be used to approximate the far-field pattern in the low-frequency theory. Moreover, an optical theorem is recovered as a corollary of the general scattering theorem. Finally, we obtain a mixed reciprocity relation which can be used in proving the uniqueness results of the inverse scattering problems. Full article
(This article belongs to the Special Issue Wave Scattering and Differential Equations)
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