Manuscript Topics

Mathematical analysis and applied mathematics are at the core of understanding and solving complex problems in both theoretical and applied sciences. This call for papers invites contributions that explore advanced mathematical techniques and methodologies in the analysis of dynamical systems, with a specific focus on partial differential equations (PDEs) and their applications to physical systems. We welcome research that bridges mathematical theory with practical problems in physics, engineering, and other applied fields.

Topics of interest include, but are not limited to:

Mathematical Analysis:

* *Partial Differential Equations (PDEs): Theoretical and numerical analysis of PDEs, including existence, uniqueness, and regularity results for elliptic, parabolic, and hyperbolic equations.
* *Singularities and Blow-up Solutions: The study of singularities, blow-up phenomena, and asymptotic behavior of solutions to nonlinear PDEs.
* *Nonlinear Analysis: Methods for analyzing nonlinear PDEs and systems of equations arising in physics and engineering.
* *Functional Analysis in PDEs: Application of functional analysis techniques, including Sobolev spaces, weak solutions, and variational methods to PDEs.
* *Fractional calculus and stochastic PDEs: Study of fractional differential equations and their applications in modeling memory effects, anomalous diffusion, and complex systems, as well as the analysis of stochastic partial differential equations in random or noisy environments.
* *Inverse Problems: Mathematical techniques for solving inverse problems, such as parameter identification and reconstruction of fields from partial observations.

Applied Mathematics:

* *Applications of PDEs in Physics: Mathematical modeling and analysis of physical phenomena, including heat conduction, wave propagation, fluid dynamics, elasticity, and electromagnetism.  
* *Biomechanics and Mathematical Biology: The application of mathematical analysis and PDEs to describe biological phenomena, such as tissue growth, fluid flow in the circulatory system, and population dynamics.  
* *Environmental Science and Climate Modeling: Mathematical models and numerical methods applied to climate dynamics, weather prediction, and ecological systems.  
* *Fluid Dynamics: Mathematical analysis of incompressible and compressible fluid flows, including Navier-Stokes equations, turbulence, and multi-phase flows.  
* *Mathematical Modeling in Engineering: Application of PDEs to problems in mechanical, civil, and electrical engineering, including structural analysis and material science.  
* *Multiscale Modeling: Techniques for modeling phenomena occurring at different scales, from molecular to macroscopic, and their description via PDEs.  
* *Numerical Methods for PDEs: Development and analysis of numerical methods for solving PDEs, including finite element methods, finite difference methods, and spectral methods.  
* *Quantum Mechanics and PDEs: The use of PDEs in quantum mechanics, including Schrödinger equations and quantum field theory.  
* *Transport and Diffusion Processes: Mathematical approaches to transport equations, diffusion phenomena, and anomalous diffusion in various settings.

We invite submissions that advance both theoretical and computational aspects of mathematical analysis, with an emphasis on real-world applications in physics and engineering. Contributions from interdisciplinary fields where mathematical analysis plays a crucial role in understanding complex systems are also encouraged.

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