The wave equation with Wentzell-Robin boundary conditions on \(L^{p}\)-spaces
type: Item
instance of: scholarly article
title: The wave equation with Wentzell-Robin boundary conditions on \(L^{p}\)-spaces
zbMATH Open document ID: 1103.47035
author: Valentin Keyantuo
author: Mahamadi Warma
published in: Journal of Differential Equations
publication date: 2006-11-15T00:00:00Z
review text: One proves that a realization of the second order differential operator \(A=au''+bu'+cu\) with Dirichlet, Neumann as well as with generalized Wentzell-Robin boundary conditions generates a cosine function on some suitable \(L^p\)-spaces. Pure Wentzell boundary conditions are considered too. The paper ends with some historical remarks on Wentzell boundary conditions.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 47D09
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D62
zbMATH DE Number: 5072904
zbMATH Keywords: Wave equation
zbMATH Keywords: Cosine function
zbMATH Keywords: Integrated semigroups
zbMATH Keywords: Wentzell-Robin boundary conditions
MaRDI profile type: Publication
full work available at URL: j.jde.2006.03.018
OpenAlex ID: W2011529148
cites work: Q2716079
cites work: Q3830008
cites work: The Laplacian with Wentzell-Robin boundary conditions on spaces of continuous functions
cites work: Abstract wave equations with generalized Wentzell boundary conditions
cites work: Q3993273
cites work: Trace theorems for holomorphic semigroups and the second order Cauchy problem
cites work: The Laplacian on \(C(\overline\Omega)\) with generalized Wentzell boundary conditions
cites work: Q3678037
cites work: Q4821158
cites work: Q4539461
cites work: The heat equation with generalized Wentzell boundary condition.
cites work: $C_0$-semigroups generated by second order differential operators with general Wentzell boundary conditions
cites work: Q4514191
cites work: The heat equation with nonlinear general Wentzell boundary condition
cites work: Generalized second order differential operators and their lateral conditions
cites work: The parabolic differential equations and the associated semigroups of transformation
cites work: Q4040640
cites work: Integrated semigroups and differential operators on \(L^ p\) spaces
cites work: The Laplace transform and the ascent method for abstract wave equations
cites work: The wave equation in \(L^{p}\)-spaces
cites work: Q4531961
cites work: Q4354419
cites work: \(L^p\) estimates for the waves equation
cites work: Q3262584
cites work: Q3238535
cites work: Wentzell-Robin boundary conditions on \(C[0,1]\)
cites work: The Robin and Wentzell-Robin Laplacians on Lipschitz domains
cites work: A solution to an open problem for wave equations with generalized Wentzell boundary conditions
cites work: The Cauchy problem for higher-order abstract differential equations
DOI: 10.1016/J.JDE.2006.03.018
description: scientific article; zbMATH DE number 5072904