Differential Equations on Manifolds and Mathematical Physics

Parametrix and localized solutions for linearized equations of gas dynamics. - Laplacians on generalized smooth distributions as C*-algebra multipliers. - C*-algebras generated by dynamical systems, and applications to nonlocal PDO. - The equivariant Atiyah-Patodi-Singer theorem. - Representations of Maslov' s canonical operator in a neighborhood of caustics. - Resurgent analysis of singularly perturbed differential systems. - Dual linear programming problem and one-dimensional Gromov minimal fillings. - Complete semiclassical spectral asymptotics for periodic and almost periodic perturbations of constant operators. - Analytic properties of the Hörmander solution of the wave equation. - Derivations of group algebras and Hohschild cohomology. - Mellin operators in weighted corner Sobolev spaces. - Quantum Hall effect and noncommutative geometry. - Flat vector bundles and open coverings. - A class of Fredholm boundary value problems for the wave equation with conditions on the entire boundary. - Motion of mechanical systems across the singular points. - Large-time decay of solutions to the Kawahara equation. - Applications of the Maslov index to phase reconstruction problems. - The complex homotopy principle of Grauert and Gromov for algebras of pseudo differential operators. - On the Fredholm solvability of operators associated with Morse-Smale diffeomorphisms. - Geometrical model of the one-dimensional double pendulum phase space. - Solutions for a nonlinear elliptic problem involving a variable exponent and measure data in unbounded domains. - Periodic internal layers in reaction-diffusion-advection equations with modular type advection. - Model of protosphera. - Pseudo-differential operators, equations, and elliptic boundary value problems.