Preliminaries; Contents; Wave Maps and Ill-posedness of their Cauchy Problem; On the Global Behavior of Classical Solutions to Coupled Systems of Semilinear Wave Equations; Decay and Global Existence for Nonlinear Wave Equations with Localized Dissipations in General Exterior Domains; Global Existence in the Cauchy Problem for Nonlinear Wave Equations with Variable Speed of Propagation; On the Global Behavior of Classical Solutions to Coupled Systems of Semilinear Wave Equations; Decay and Global Existence for Nonlinear Wave Equations with Localized Dissipations in General Exterior Domains
Summary
Presenting several developments in the theory of hyperbolic equations, this book's contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods
