Current Trends in Nonlinear Partial Differential Equations
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".
Deadline for manuscript submissions: 30 April 2027 | Viewed by 48
Editors
Interests: nonlinear PDEs; mathematical fluid dynamics; applied mathematics
2. School of Mathematics, University of Birmingham, Watson Building, Edgbaston, Birmingham B15 2TT, UK
Interests: nonlinear PDEs; harmonic analysis; nonlinear Schrödinger equations
Special Issue Information
Dear Colleagues,
Nonlinear partial differential equations (PDEs) constitute one of the most active and influential research areas in modern mathematics. They provide fundamental mathematical models for a wide range of phenomena in the natural sciences, engineering, economics, and other disciplines, while also giving rise to challenging theoretical problems that stimulate the development of new analytical techniques and mathematical theories.
In recent years, remarkable progress has been achieved in the study of nonlinear PDEs through advances in functional analysis, variational methods, geometric analysis, harmonic analysis, and numerical computation. Emerging topics such as nonlocal and fractional models, stochastic and random effects, free boundary problems, geometric flows, and data-driven approaches have further expanded the scope of nonlinear PDE research, creating new connections between pure and applied mathematics.
This Special Issue aims to provide a forum for presenting current advances, new methodologies, and emerging trends in nonlinear partial differential equations. We welcome original research articles and comprehensive review papers that contribute to the theoretical analysis, computational methods, and mathematical modeling of nonlinear PDEs. Particular emphasis is placed on rigorous mathematical analysis, innovative analytical techniques, and interdisciplinary applications that promote further developments in this rapidly evolving field.
Topics of interest include, but are not limited to, the following:
- Nonlinear elliptic, parabolic, and hyperbolic equations;
- Existence, uniqueness, regularity, and qualitative properties of solutions;
- Stability, asymptotic behavior, and long-time dynamics;
- Variational methods, critical point theory, and topological methods;
- Nonlocal, fractional, and integro-differential equations;
- Geometric partial differential equations and geometric flows;
- Reaction–diffusion systems, conservation laws, and nonlinear wave equations;
- Free boundary problems and moving interface models;
- Stochastic partial differential equations;
- Numerical analysis and computational methods for nonlinear PDEs;
- Inverse problems, optimal control, and optimization involving PDEs.
Prof. Dr. Wendong Wang
Dr. Yuzhao Wang
Guest Editors
Manuscript Submission Information
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Keywords
- nonlinear partial differential equations
- regularity theory
- variational methods
- fluid dynamics
- stability analysis
- nonlinear Schrödinger equations
- stochastic and fractional PDEs
- fractional PDEs
- mathematical analysis
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