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

Abstract

We study the parabolic Lame 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 D'operateurs lineaires et equations differentielles operationnelles, 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 Lame system with parameter. We show that the remainder has the H-2,H-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. (C) 2013 Elsevier Inc. All rights reserved.