New Advances in Mathematical Analysis and Applications

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

Deadline for manuscript submissions: 30 November 2026 | Viewed by 782

Special Issue Editors


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Guest Editor
Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Interests: numerical modeling; applied mathematics engineering; applied and computational mathematics; mathematical modelling; modeling and simulation; algorithms; numerical analysis; numerical mathematics; mathematical analysis; nonlinear dynamics

E-Mail Website
Guest Editor
Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Interests: data modeling; database; differential equations; partial differential equation

Special Issue Information

Dear Colleagues,

The Special Issue “New Advances in Mathematical Analysis and Applications” aims to present recent developments in theoretical and applied aspects of mathematical analysis and its applications in science and engineering.

The Special Issue will focus on modern analytical methods, numerical techniques, and mathematical models that address nonlinear phenomena, differential equations, dynamical systems, and computational challenges arising in real-world problems.

Topics of interest include, but are not limited to, the following: qualitative analysis of differential equations; numerical methods for ordinary and partial differential equations; stability and convergence analysis; nonlinear dynamics; mathematical modeling in physics, engineering, and applied sciences.

The Special Issue seeks contributions that combine rigorous mathematical analysis with practical applications, as well as works that introduce new computational approaches or extend classical analytical results to contemporary problems.

Dr. Pavlina Atanasova
Dr. Magdalena Veselinova
Guest Editors

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Keywords

  • numerical analysis
  • mathematical analysis
  • differential equations
  • nonlinear dynamics
  • mathematical modeling
  • computational mathematics numerical methods

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Published Papers (1 paper)

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Research

14 pages, 273 KB  
Article
Exponential Stability of Swelling Soils with Thermodiffusion Effects
by Arar Mutlag A. Alajmi and Tijani A. Apalara
Mathematics 2026, 14(7), 1184; https://doi.org/10.3390/math14071184 - 1 Apr 2026
Viewed by 611
Abstract
In this work, we study a one-dimensional coupled hyperbolic–parabolic system modeling the dynamics of swelling soils under thermodiffusion effects. The model describes the interaction between the deformation of the solid skeleton, the pore fluid motion, the temperature variation, and a diffusive process formulated [...] Read more.
In this work, we study a one-dimensional coupled hyperbolic–parabolic system modeling the dynamics of swelling soils under thermodiffusion effects. The model describes the interaction between the deformation of the solid skeleton, the pore fluid motion, the temperature variation, and a diffusive process formulated through chemical potential. Under mixed boundary conditions and without introducing additional mechanical damping or imposing restrictive relations among the physical parameters, we prove exponential stability of the system. Our analysis is based on the energy method. In contrast to the standard energy functional commonly used in related thermodiffusion models, we introduce a modified positive energy functional better adapted to the coupled structure of the system. By combining this energy with suitable auxiliary functionals, we construct an appropriate Lyapunov functional and derive an exponential stability estimate. Our result shows that thermodiffusion alone yields sufficient dissipation for exponential stabilization, complementing earlier works where exponential stability requires extra damping mechanisms or equal wave-speed assumptions. Full article
(This article belongs to the Special Issue New Advances in Mathematical Analysis and Applications)
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