This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics.

The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.

Inhalt
Some Applications of a Closed-form Solution for Compound Options of Order N.- Surjective Linear Partial Differential Operators with Variable Coefficients on Non-quasianalytic Classes of Roumieu Type.- The Fundamental Solution for a Second Order Weakly Hyperbolic Cauchy problem.- Pseudoholomorphic Discs Attached to Pseudoconcave Domains.- Vorticity and Regularity for Solutions of Initial-boundary Value Problems for the NavierStokes Equations.- Exponential Decay and Regularity for SG-elliptic Operators with Polynomial Coefficients.- A Short Description of Kinetic Models for Chemotaxis.- Eigenvalues, Eigenfunctions in Domains Becoming Unbounded.- Loss of Derivatives for t?? in Strictly Hyperbolic Cauchy Problems.- On the Operator Splitting Method: Nonlinear Balance Laws and a Generalization of Trotter-Kato Formulas.- Subelliptic Estimates for some Systems of Complex Vector Fields.- Approximate Solutions to the 2-D Unsteady Navier-Stokes System with Free Surface.- Time Decay Estimates of Solutions for Wave Equations with Variable Coefficients.- On Weakly Pseudoconcave CR Manifolds.- A Note on Kohn's and Christ's Examples.- On the Nonstationary Two-dimensional Navier-Stokes Problem in Domains with Strip-like Outlets to Infinity.- A Link between Local Solvability and Partial Analyticity of Several Classes of Degenerate Parabolic Operators.- The Solution of the Equation with .- On Schauder Estimates for the Evolution Generalized Stokes Problem.- Local Analyticity and Nonlinear Vector Fields.- Strongly Hyperbolic Complex Systems Reduced Dimension, Hermitian Systems.