Evolution Inclusions and Variation Inequalities for Earth Data Processing III: Long-Time Behavior of Evolution Inclusions Solutions in Earth Data Analysis
Springer Science & Business Media, May 22, 2012 - Mathematics - 330 pages
In this sequel to two earlier volumes, the authors now focus on the long-time behavior of evolution inclusions, based on the theory of extremal solutions to differential-operator problems. This approach is used to solve problems in climate research, geophysics, aerohydrodynamics, chemical kinetics or fluid dynamics. As in the previous volumes, the authors present a toolbox of mathematical equations. The book is based on seminars and lecture courses on multi-valued and non-linear analysis and their geophysical application.
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ˇ ˇ ˇ 3D Navier–Stokes a.e. t G arbitrary attractors of multivalued Banach space bounded set closed set continuous continuous embedding convergence convex Corollary Cv.X deﬁned deﬁnition denote Differ Equat differential equations differential-operator inclusions dynamical systems embedding evolution inclusions exists ﬁxed follows function G R+ global attractor global compact hemivariational inequalities Hence Hilbert space initial data Kapustyan Kasyanov kykX Lemma Let us consider Let us prove linear m-semiflow Math Anal Appl mathematical Melnik Moreover multivalued dynamical multivalued map multivalued semiflows Navier–Stokes equations negatively semiinvariant nonautonomous nonempty obtain operator optimal Papageorgiou phase space piezoelectric precompact Proof Proposition pseudomonotone pullback attractor reaction-diffusion equations Remark satisﬁes semigroup sequence subsequence subset Theorem theory topology trajectory attractor uniqueness upper semicontinuous Valero variational inequalities Vt G weak solution weakly