Applied Mathematical Sciences: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations

P. Constantin · C. Foias · B. Nicolaenko · R. Temam

2012년 12월 · Applied Mathematical Sciences 70호 · Springer Science & Business Media

eBook

123

페이지

검증되지 않은 평점과 리뷰입니다. 자세히 알아보기

eBook 정보

This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.