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.
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.
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. Obrechts 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.
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