Existence for wave equations on domains with arbitrary growing cracks
type: Item
instance of: scholarly article
title: Existence for wave equations on domains with arbitrary growing cracks
zbMATH Open document ID: 1239.35086
DOI: 10.4171/RLM/606
author: G. Dal Maso
author: Christopher J. Larsen
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2012-05-08T00:00:00Z
review text: Summary: We formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 74J05
Mathematics Subject Classification ID: 74R10
zbMATH DE Number: 6031543
zbMATH Keywords: zero Neumann condition
zbMATH Keywords: damped and undamped equations
zbMATH Keywords: dynamic fracture mechanics
zbMATH Keywords: cracking domains
zbMATH Keywords: special functions with bounded variation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6031543