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On the Eshelby-Kostrov property for the wave equation in the plane


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


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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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