Manuscript Topics

Hyperbolic partial differential equations form a cornerstone of modern partial differential equations theory, arising naturally in general relativity, quantum mechanics, hydrodynamics, electromagnetics, elastic mechanics, and other related fields. They describe phenomena where disturbances propagate at finite speeds, primarily wave motion. Key features include the formation and travel of waves, the confinement of influences within characteristic cones, and—in nonlinear cases—the spontaneous emergence of shock waves, rarefaction waves, or discontinuities from smooth initial conditions. These equations also exhibit reflection, refraction, interference, and, in dispersive media, frequency-dependent wave separation. Despite significant progress, many fundamental issues remain open, particularly concerning initial-boundary value problems, coupled systems, and physically relevant stability analysis.

This special issue seeks original research articles and comprehensive reviews that advance the theoretical understanding of hyperbolic partial differential equations and their coupled systems, with particular emphasis on problems motivated by physics and engineering. Analytical approaches that address existence, stability, uniqueness, asymptotic behavior, or other properties are welcome.

Topics of interest include, but are not limited to:
1. Formation of singularities and global wellposedness;
2. Boundary conditions and compatibility conditions;
3. Hyperbolic-elliptic systems;
4. Hyperbolic-parabolic systems;
5. Hyperbolic conservation laws;
6. Linear and nonlinear stability of nonlinear waves;
7. Applications to magnetohydrodynamics (MHD), relativistic fluids, plasmas, elasticity, and biological systems;
8. Stability of coupled interfaces and mixed-type PDEs;
9. Degenerate hyperbolic equations and boundary layer analysis

Instructions for authors
https://www.aimspress.com/era/news/solo-detail/instructionsforauthors
Please submit your manuscript to online submission system
https://aimspress.jams.pub/