### Impacto

### Downloads

Downloads per month over past year

Herrero, Miguel A. and Oleaga Apadula, Gerardo Enrique and Velázquez, J.J. L.
(2006)
*On the Eshelby-Kostrov property for the wave equation in the plane.*
Transactions of the American Mathematical Society, 358
(8).
pp. 3673-3695.
ISSN 1088-6850

Preview |
PDF
251kB |

Official URL: http://dialnet.unirioja.es/servlet/revista?codigo=1445

## Abstract

This work deals with the linear wave equation considered in the whole plane R2 except for a rectilinear moving slit, represented by a curve Γ (t) = {(x1, 0) : −∞ < x1 < λ(t)} with t ≥ 0. Along Γ (t) , either homogeneous Dirichlet or Neumann boundary conditions are imposed. We discuss existence and uniqueness for these problems, and derive explicit representation formulae for solutions. These last have a simple geometrical interpretation, and in particular allow to derive precise asymptotic expansions for solutions near the tip of the curve. In the Neumann case, we thus recover a classical result in fracture dynamics, namely the form of the stress intensity factor in crack propagation under antiplane shear conditions

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Stress Intensity Factors; Crack Paths; Propagation; Evolution; Situations; Expansion; Form |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 12899 |

Deposited On: | 29 Jun 2011 09:35 |

Last Modified: | 12 Dec 2018 15:07 |

### Origin of downloads

Repository Staff Only: item control page