Some Aspects of an Integrodifferential Equation: the Weertman Equation

  • Marc Josien (CERMICS, ENPC)
A3 01 (Sophus-Lie room)


The Weertman equation is a nonlinear integrodifferential equation which models steadily-moving dislocations in materials science. Its solution can be interpreted as the (unique) traveling wave of an "artificial" dynamical system (a nonlocal reaction-diffusion

equation). Under reasonable hypotheses, we prove that, for any initial condition, the dynamical system actually converges to the solution of the Weertman equation. That convergence provides a way of approximating numerically this solution.

Joint work with: Y.-P. Pellegrini (CEA-DAM), F. Legoll (ENPC), C. Le Bris (ENPC).