Topics on stability and periodicity in abstract differential equations

Description

This volume presents a unified theory of shock waves corresponding to gravitational and electromagnetic fields and to magnetohydrodynamics in the context of general relativity. The common tool employed is provided by tensor distribution -- an approach which has been systematically developed by the author since 1962. One remarkable result is that this yields a complete theory of magnetohydrodynamic shock waves, which can also be applied to the treatment of pulsars. The same method is also applicable to the quantization of some physical fields in curved space-time. This, too, is discussed in the book. For graduate students and researchers in mathematical physics and theoretical astrophysics "This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas."--BOOK JACKET.  Read more... Banach spaces and linear operators -- Strongly continuous semigroups of operators -- Spectral theory -- Stability and exponential dichotomy -- Perron theorem -- Evolution semigroups and Perron theorem -- Stability theory -- Almost periodic solutions -- Evolution semigroups & periodic equations -- Sums of commuting operators -- Decomposition theorem -- Almost automorphic solutions -- The inhomogeneous linear equation -- Method of invariant subspaces and almost automorphic solutions of second-order differential equations -- Existence of almost automorphic solutions to semilinear differential equations -- Method of sums of commuting operators and almost automorphic functions -- Almost automorphic solutions of second order evolution equations -- The equations x'=f(t,x) -- Nonlinear equations -- Periodic solutions of nonlinear equations -- Evolution semigroups and almost periodic solutions