Zusammenfassung für den Vortrag am 19.04.2018 (11:00 Uhr)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Marc Josien (CERMICS, ENPC)
Some Aspects of an Integrodifferential Equation: the Weertman Equation
Joint work with: Y.-P. Pellegrini (CEA-DAM), F. Legoll (ENPC), C. Le Bris (ENPC).
Abstract: 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.