For the parabolic Lamé 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 Dʼoperateurs 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 , 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.

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