This subtopic studies general topics in partial differential equations, including foundational frameworks, classification, and basic analytic principles.

This subtopic studies qualitative properties of PDEs, focusing on existence, uniqueness, regularity, and broad structural features of solutions.

This subtopic studies representations of solutions to PDEs, including integral formulas, Green function methods, and transform techniques.

This subtopic studies generalized solutions of PDEs, where weak, distributional, or variational formulations extend classical solution concepts.

This subtopic studies PDEs with constant or variable coefficients, emphasizing how coefficient structure affects solvability and behavior.

This subtopic studies first-order PDEs, including method-of-characteristics techniques and the geometry of solution curves.

This subtopic studies higher-order PDEs, focusing on equations of order greater than one and the analytic methods used to solve them.

This subtopic studies PDEs close to elliptic equations, where near-ellipticity guides regularity, solvability, and perturbation arguments.

This subtopic studies elliptic equations and systems, emphasizing regularity, maximum principles, boundary behavior, and the analytic structure of solutions.

This subtopic studies parabolic equations and systems, focusing on evolution problems, smoothing effects, positivity, and long-time behavior.

This subtopic studies hyperbolic equations and systems, with emphasis on wave propagation, finite-speed effects, energy estimates, and geometry.

This subtopic studies mixed-type and composite-type equations, where the governing operator changes character across regions of the domain.

This subtopic studies overdetermined systems, focusing on compatibility conditions, solvability constraints, and the structure of solutions when data exceed the expected freedom.

This subtopic studies spectral theory and eigenvalue problems for PDEs, including variational methods, resonance phenomena, and qualitative properties of spectra.

This subtopic studies PDEs in connection with mathematical physics, including models for fluids, waves, optics, quantum systems, and other continuum phenomena.

This subtopic gathers miscellaneous PDE topics that connect the theory of partial differential equations with broader analytic, geometric, and applied methods.

This subtopic studies pseudodifferential operators and related symbolic methods, which provide a flexible framework for handling singular and nonlocal effects in PDE theory.