Differential Equations in Banach Spaces

by Giovanni Dore (Editor)

Overview

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.

Product Details

ISBN-13:	9781138413214
Publisher:	Taylor & Francis
Publication date:	08/02/2017
Series:	Lecture Notes in Pure and Applied Mathematics
Pages:	286
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

GIOVANNI DORE is Associate Professor of Mathematical Analysis at the University of Bologna, Italy. He is the author of several professional papers on differential equations in Banach spaces and interpolation theory, among other subjects. Dr. Dore received the Lau- rea (1978) in mathematics from the University of Bologna. ANGELO FAVINI is Professor of Mathematical Analysis at the University of Bologna, Italy. His research interests focus on functional analysis, operator theory, differential equations in Banach spaces, and degenerate differential equations. He received the Laurea (1969) in mathematics from the University of Bologna. ENRICO OBRECHT is Professor of Mathematical Analysis at the University of Bologna, Italy. Dr. Obrecht’s research emphasizes boundary value problems for elliptic and parabolic partial differential equations and differential equations in Banach spaces, particularly for orders greater than one. He received the Laurea (1971) in mathematics from the University of Bologna. ALBERTO VENNI is Associate Professor of Mathematical Analysis at the University of Bologna, Italy. His research interests involve functional analysis, operator theory, and dif¬ferential equations in Banach spaces. Dr. Venni received the Laurea (1973) in mathematics from the University of Bologna.

Table of Contents

Preface — Contributors — Conference Participants — Abstract Linear Nonautonomous Parabolic :Equations: A Survey Paolo Acquistapace — On Some Classes of Singular Variational Inequalities Marco Luigi Bernardi and Fabio Luterotti — Nonuniqueness in L 00: An Example Julio E. Bouillet — Some Results on Abstract Evolution :Equations of Hyperbolic Type Piennarco 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 a von Karman System with Boundary Damping /A. Favini and I. Lasiecka — Linear Parabolic Differential :Equations of Higher Order in Time /A. 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 Albrecht Holderrieth — Uniform Decay Rates for Semilinear Wave Equations with Nonlinear and Nonmonotone Boundary Feedback, without Geometric Conditions /I. Lasiecka and D. Tataro — Sharp Trace Estimates of Solutions to Kirchhoff and Euler-Bernoulli Equations /I. Lasiecka and R. Triggiani — Boundary Values of Holomorphic Semigroups, H00 Functional Calculi, and the Inhomogeneous Abstract Cauchy Problem Ralph deLaubenjels — Stability of Linear Evolutionary Systems with Applications to Viscoelasticity Jan Pruss — Generation of Analytic Semigroups by Variational Operators with L 00 Coefficients Vincenzo Vespri — Asynchronous Exponential Growth in Differential Equations with Homogeneous Nonlinearities /G. F. Webb — Inversion of the Vector-Valued Laplace Transform in L,(X)-Spaces /L. Weis — Some Quasilinear Parabolic Problems in Applied Mathematics Atsushi Yagi — Index.

Editorial Reviews

Proceedings of a conference in Bologna, Italy in 1991. Topics discussed include abstract linear nonautonomous parabolic equations, some classes of singular variational inequalities, results on abstract evolution equations of hyperbolic type, interpolation and extrapolation spaces and parabolic equations, diagonalization of certain operator matrices related to Volterra equations, linear parabolic differential equations of higher order in time, and multiplicative perturbation of resolvent positive operators. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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