International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 92134, 26 pages
doi:10.1155/IJMMS/2006/92134
Maximal regular boundary value problems in Banach-valued
function spaces and applications
Department of Electrical-Electronics Engineering, Faculty of Engineering, Istanbul University, Avcilar, Istanbul 34320, Turkey
Received 27 December 2004; Accepted 30 September 2005
Copyright © 2006 Veli B. Shakhmurov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The nonlocal boundary value problems for differential operator
equations of second order with dependent coefficients are studied.
The principal parts of the differential operators generated by
these problems are non-selfadjoint. Several conditions for the
maximal regularity and the Fredholmness in Banach-valued
Lp-spaces of these problems are given. By using these
results, the maximal regularity of parabolic nonlocal initial
boundary value problems is shown. In applications, the nonlocal
boundary value problems for quasi elliptic partial differential
equations, nonlocal initial boundary value problems for parabolic
equations, and their systems on cylindrical domain are
studied.