an:00152096
Zbl 0783.35024
Maghnouji, Abderrahman
Parabolic boundary value problems on a nonsmooth domain
FR
C. R. Acad. Sci., Paris, S??r. I 316, No. 4, 331-336 (1993).
00011840
1993
j
35K35 35C99 35D10
decomposition of solutions; first order evolution equation; elliptic operators of even order in polygons
Summary: It is well known that the solution of a boundary value problem on a domain with a conical singularity admits a decomposition into a singular part and a regular one (see for instance the results of Kondrat'ev, Maz'ya-Plamenevskij, Grisvard and Dauge). Here we get analogous decomposition for parabolic problems on a cylinder with a polygonal basis. We extend on one hand the results of M. Moussaoui and B. K. Sadallah, P. Grisvard and A. Hammoudi concerning the heat equation and on the other hand those of V. S. Agranovich and M. I. Vishik and J.-L. Lions, where general parabolic problems are treated on smooth domains.