Includes bibliographical references (pages 221-223) and index.
Contents:
Introduction -- Differential Equations in Hilbert Space -- Linear Parabolic Systems: Basic Theory -- Elliptic Systems: Higher Order Regularity -- Parabolic Systems: Higher Order Regularity -- Applications to Quasilinear Systems -- Appendix: Selected Topics in Analysis.
Summary:
This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces.--Publisher's information.
Series:
Mathematical surveys and monographs, 0076-5376 ; volume 251
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.