Analytic and Gevrey Well-Posedness of the Cauchy Problem for Second Order Weakly Hyperbolic Equations with Coefficients Irregular in Time

Publisher Summary This chapter focuses on the interplay between the structure of Banach scale, in which it is possible to solve the abstract Kovalewskian problems locally, and the one of Hilbert triplet, where the global solvability for the strictly hyperbolic second order equations can be set. It discusses the connections between weak hyperbolicity and analytic well-posedness or between strict hyperbolicity and C ∞ -well-posedness. The chapter explains global solvability in the class of analytic functions of some nonlinear equations of hyperbolic type such as the integrodifferential equation.