For the parabolic Lamé system on polygonal domains: The transport equation

Abstract

We study the parabolic Lamé system with initial and boundary conditions on non-convex plane polygonal domains. We express the solution by the inverse of the sum of two operators taken from [G. Da Prato, P. Grisvard, Sommes Dʼopérateurs linéaires et équations différentielles opérationnelles, J. Math. Pures Appl. 54 (1975) 305–387] and split the solution into a singular part and a regular part by applying to the inverse the corner singularity result of the Lamé system with parameter. We show that the remainder has the H2,q-regularity and that the coefficients of the corner singularities, so-called the stress intensity factors, have the fractional order regularities on the time interval. Also we investigate the transport equation directed by the vector field having the corner singularity decomposition.