Symmetry in Mathematical Theory and Simulation Methods for Backward Problems

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

Deadline for manuscript submissions: 31 July 2024 | Viewed by 1598

Special Issue Editor

Department of Mechanical Engineering, National United University, Miaoli 36063, Taiwan
Interests: numerical analysis, fluid mechanics, thermodynamics, dynamic system, plasticity, friction dynamics, inverse/backward problems, ordinary differential equations, partial differential equations, Lie algebra, Lie-group numerical methods

Special Issue Information

Dear Colleagues,

Backward problems have been investigated in science, mathematics, and engineering, and reveal an unknown property of an object from their experimentation or observation. Backward problems conform to the Symmetry journal's ideology as they are the opposite of the associated forward issue, which concerns the cause­–effect relationship.

Backward problems have a wide range of applications, including mechanics, heat conduction, acoustics, semiconductors, medical imaging, nondestructive testing, physics, systems biology, finance, robotics, computer vision, radar, thermoelastics, and groundwater.

This Special Issue of Symmetry concentrates on the present mathematical theory and simulation regarding backward problems and how they relate to their applications in engineering and science.

Dr. Chih-Wen Chang
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 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

  • backward problems
  • inverse problems
  • numerical analysis
  • mathematical modeling
  • fractional problems
  • ordinary/partial differential equations
  • meshless methods
  • applications
  • symmetry operators

Published Papers (1 paper)

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Research

28 pages, 418 KiB  
Article
Noncommutative Integration of Generalized Diffusion PDE
by Sergey Victor Ludkowski
Symmetry 2022, 14(10), 2049; https://doi.org/10.3390/sym14102049 - 01 Oct 2022
Viewed by 826
Abstract
The article is devoted to the noncommutative integration of a diffusion partial differential equation (PDE). Its generalizations are also studied. This is motivated by the fact that many existing approaches for solutions of PDEs are based on evolutionary operators obtained as solutions of [...] Read more.
The article is devoted to the noncommutative integration of a diffusion partial differential equation (PDE). Its generalizations are also studied. This is motivated by the fact that many existing approaches for solutions of PDEs are based on evolutionary operators obtained as solutions of the corresponding stochastic PDEs. However, this is restricted to PDEs of an order not higher than 2 over the real or complex field. This article is aimed at extending such approaches to PDEs of an order higher than 2. For this purpose, measures and random functions having values in modules over complexified Cayley–Dickson algebras are investigated. Noncommutative integrals of hypercomplex random functions are investigated. By using them, the noncommutative integration of the generalized diffusion PDE is scrutinized. Possibilities are indicated for a subsequent solution of higher-order PDEs using their decompositions and noncommutative integration. Full article
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