Differential Equations in Banach Spaces

Giovanni Dore, Angelo Favini, Enrico Obrecht, Alberto Venni

• Publisher: CRC Press
• Year: 2020
• eBook ISBN: 9781000153651
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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.

Sharp Trace Estimates of Solutions to Kirchhoff and Euler-Bernoulli Equations

I. LASIECKA Department of Applied Mathematics, University of Virginia, Charlottesville, VA 22903, U.S.A.

R. TRIGGIANI Department of Applied Mathematics, University of Virginia, Charlottesville, VA 22903, U.S.A.

1. Introduction: A Wave Problem

Let Ω be an open bounded domain in Rⁿ with smooth boundary Γ. Let $-A(\text{x},\partial )$ be a second-order elliptic operator of order two with smooth, space variable coefficients. Consider the second - order hyperbolic equation in w(t,x):

${\text{w}}_{\text{t}\text{t}}=A(\text{x},\partial )\text{w}\text{in}(0,\text{T}]\times \text{Ω}={\text{Q}}_{\text{T}}.$

(1.1)

The following estimate on the tangential trace $\frac{\partial }{\partial \text{τ}}\text{w}$ of (smooth) solutions of...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Preface
• Table of Contents
• Contributors
• Conference Participants
• Abstract Linear Nonautonomous Parabolic Equations: A Survey
• On Some Classes of Singular Variational Inequalities
• Nonuniqueness in L∞: An Example
• Some Results on Abstract Evolution Equations of Hyperbolic Type
• Interpolation and Extrapolation Spaces and Parabolic Equations
• On the Diagonalization of Certain Operator Matrices Related to Volterra Equations
• Second Order Abstract Equations with Nonlinear Boundary Conditions: Applications to a von Karmàn System with Boundary Damping
• Linear Parabolic Differential Equations of Higher Order in Time
• Analytic and Gevrey Class Semigroups Generated by -A + iB, and Applications
• The Kompaneets Equation
• Multiplicative Perturbation of Resolvent Positive Operators
• Uniform Decay Rates for Semilinear Wave Equations with Nonlinear and Nonmonotone Boundary Feedback, without Geometric Conditions
• Sharp Trace Estimates of Solutions to Kirchhoff and Euler-Bernoulli Equations
• Boundary Values of Holomorphic Semigroups, H∞ Functional Calculi, and the Inhomogeneous Abstract Cauchy Problem
• Stability of Linear Evolutionary Systems with Applications to Viscoelasticity
• Generation of Analytic Semigroups by Variational Operators with L°° Coefficients
• Asynchronous Exponential Growth in Differential Equations with Homogeneous Nonlinearities
• Inversion of the Vector-Valued Laplace Transform in Lp(X)-Spaces
• Some Quasilinear Parabolic Problems in Applied Mathematics
• Index