2026-06-27T10:58:59Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/497052023-08-26T19:01:25Zcom_20.500.14352_14col_20.500.14352_15

On the Eshelby-Kostrov property for the wave equation in the plane Herrero, Miguel A. Oleaga Apadula, Gerardo Enrique Velázquez, J.J. L. 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 2023-06-20T09:29:24Z 2023-06-20T09:29:24Z 2023-06-20T09:29:24Z 2006 journal article https://hdl.handle.net/20.500.14352/49705 1088-6850 10.1090/S0002-9947-06-03995-X eng open access American Mathematical Society