Advances in Partial Differential Equations and Functional Analysis

Dear Colleagues,

The Special Issue ‘Advances in Partial Differential Equations and Functional Analysis’ is dedicated to recent progress and new ideas in the important field of Analysis. Analysis is a central mathematical discipline, motivated by applications in Physics, Chemistry, Economy, Astrophysics, Cosmology, Quantum Mechanics, Relativity, and many other fields of practical importance. Partial Differential Equations are based on tools of Functional Analysis, and they interact with other fields, such as Geometry, Numerical Mathematics, Algebra, Topology, Probability. Microlocal analysis is important in illustrating several special aspects, particularly its use of topological vector spaces, distributions, analytic functionals, complex analysis, its relationship with symplectic geometry and classical mechanics, with applications in the propagation of singularities. Important aspects include pseudo-differential and Fourier-integral operators; electrodynamic equations; global analysis and index theory, closely related to analysis on manifolds and K-theory; operators on Lie groups; boundary value problems; inverse problems; initial value problems; equivariant theories; geometric operators such as Laplace–Beltrami operators, Dirac operators, and Laplacians, connected with (sub-)Riemannian geometries; analysis on manifolds with singularities, such as conical points or edges and corners; operators describing non-linear wave phenomena, e.g., Korteveg de Vries-type equations; studying solitary waves; equations of mixed type, e.g., the Tricomi equation, modelling sub- and super-sonic flow. There is a wide variety of problems. Let us give a few words on the functional-analytic background. This is very much formulated in connection with locally convex vector spaces, operator algebras in Hilbert-, Banach-, or more general spaces, semi-groups of operators, abstract evolution equations.

Prof. Dr. Bert Wolfgang Schulze
Guest Editor

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