On the Cauchy problem for the wave equation on time-dependent domains
type: Item
instance of: scholarly article
title: On the Cauchy problem for the wave equation on time-dependent domains
zbMATH Open document ID: 1411.35189
author: G. Dal Maso
author: Rodica Toader
published in: Journal of Differential Equations
publication date: 2019-01-22T00:00:00Z
review text: One introduces a new concept for the solution of the wave equation on a time dependent domain and compare it with the one considered in a previous paper of the authors: [Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 22, No. 3, 387--408 (2011; Zbl 1239.35086)]. The new definition is based on integration by parts in time and does not require a precise definition of the value at time \(t\) of the second derivative of \(u(t)\). Under some special assumptions on initial data, an existence result for the solution to the Cauchy problem is proved. Additional conditions assure the uniqueness of solution.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 74R10
zbMATH DE Number: 7005197
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: integration by parts in time
MaRDI profile type: Publication
full work available at URL: j.jde.2018.08.056
OpenAlex ID: W2891001935
cites work: Q5591023
cites work: Q5665783
cites work: Linear hyperbolic systems in domains with growing cracks
cites work: Quasistatic crack growth in nonlinear elasticity
cites work: Existence for wave equations on domains with arbitrary growing cracks
cites work: Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition
cites work: The Wave Equation on Domains with Cracks Growing on a Prescribed Path: Existence, Uniqueness, and Continuous Dependence on the Data
cites work: Dynamic Fracture Mechanics
cites work: Q5890172
cites work: Dynamic crack propagation in a 2D elastic body: the out-of-plane case
cites work: Compact sets in the space \(L^ p(0,T;B)\)
cites work: Weak formulation of elastodynamics in domains with growing cracks
DOI: 10.1016/J.JDE.2018.08.056
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description: scientific article; zbMATH DE number 7005197