This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.
Table of Contents
Abstract linear non-autonomous parabolic equations - a survey, Paolo Acquistapace; on some classes of singular variational inequalities, Marco Luigi Bernardi and Fabio Luterotti; non-uniqueness in L(?????) - an example, Julio E. Bouillet; some results on abstract evolution equations of hyperbolic type, Piermarco Cannarsa and Giuseppe Da Prato; interpolation and extrapolation spaces and parabolic equations, Gabriella Di Blasio; on the diagonalization of certain operator matrices related to Volterra equations, Klaus-Jochen Engel; second order abstract equations with nonlinear boundary conditions - applications to von Karman system with boundary damping, A. Favini and I. Lasiecka; linear parabolic differential equations of higher order in time, Angelo Favini and Hiroki Tanabe; analytic and gevrey class semigroups generated by -A + iB, and applications, A. Favini and R. Triggiani; the Kompaneets equation, Jerome A. Goldstein; multiplicative perturbation of resolvent positive operators, Abrecht Holderrieth; uniform decay rates for semilinear wave equations with nonlinear and nonmonotone boundary feedback - without geometric conditions, I. Lasiecka and D. Tataru; sharp trace estimates of solutions to Kirchhoff and Euler-Bernoulli equations, I. Lasiecka and R. Triggiani; boundary values of holomorphic semigroups, H(?????) functional calculi and the inhomogeneous abstract Cauchy problem, Ralph deLaubenfels; stability of linear evolutionary systems with applications to viscoelasticity, Jan Pruss; generation of analytic semigroups by variational operators with L(?????) coefficients, Vincenzo Vespri; asynchronous exponential growth in differential equations with homogeneous nonlinearities, G.F. Webb; the inversion of the vector-valued Laplace transform in L[p](X)-spaces, L. Weis; some quasilinear parabolic problems in applied mathematics, Atsushi Yagi.