Herrero, Miguel A. and Oleaga Apadula, Gerardo Enrique and Velázquez, J.J. L. (2006) On the EshelbyKostrov property for the wave equation in the plane. Transactions of the American Mathematical Society, 358 (8). pp. 36733695. ISSN 10886850

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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:  06 Feb 2014 09:35 
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