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Titlebook: Dynamics of Evolutionary Equations; George R. Sell,Yuncheng You Book 2002 Springer Science+Business Media New York 2002 Dynamical Systems.

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书目名称Dynamics of Evolutionary Equations
编辑George R. Sell,Yuncheng You
视频video
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Dynamics of Evolutionary Equations;  George R. Sell,Yuncheng You Book 2002 Springer Science+Business Media New York 2002 Dynamical Systems.
描述The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations that attempt to model phenomena that change with time. The infi­ nite dimensional aspects occur when forces that describe the motion depend on spatial variables, or on the history of the motion. In the case of spatially depen­ dent problems, the model equations are generally partial differential equations, and problems that depend on the past give rise to differential-delay equations. Because the nonlinearities occurring in thse equations need not be small, one needs good dynamical theories to understand the longtime behavior of solutions. Our basic objective in writing this book is to prepare an entree for scholars who are beginning their journey into the world of dynamical systems, especially in infinite dimensional spaces. In order to accomplish this, we start with the key concepts of a semiflow and a flow. As is well known, the basic elements of dynamical systems, such as the theory of attractors and other invariant sets, have their origins here.
出版日期Book 2002
关键词Dynamical Systems; Dynamics of Nonlinear PDE‘s; Evolutionary Equations; Infinite Dynamical Systems; Navi
版次1
doihttps://doi.org/10.1007/978-1-4757-5037-9
isbn_softcover978-1-4419-3118-4
isbn_ebook978-1-4757-5037-9Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer Science+Business Media New York 2002
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Linear Semigroups,inite dimensional versions of solutions of the finite dimensional linear ordinary differential equation ... = ..In particular, the ..-semigroup corresponds to the solution operator or the fundamental solution matrix, and the infinitesimal generator corresponds to the linear coefficient matrix .. We
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Basic Theory of Evolutionary Equations,f ..-semigroups. As we have seen, this theory allows one to construct mild solutions of many linear partial differential equations with constant coefficients. Our objective in this chapter is to generalize this theory so that it applies first to the linear inhomogeneous equation . and then the nonli
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Nonlinear Partial Differential Equations,ally interested here in those nonlinear evolutionary equations which arise in the analysis of two broad classes of partial differential equations: parabolic evolutionary equations and hyperbolic evolutionary equations. While our usage of the terms “parabolic” and “hyperbolic” in this context is moti
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Navier-Stokes Dynamics,sfer and its effects on global climate modeling and weather prediction; 2) flows of multiphased fluids and oil recovery; 3) behavior of chemical solutes in lakes, harbors and river basins; 4) geothermal consequences of magma flows; and 5) fluid flows in thin films. In order to understand the modelin
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Major Features of Dynamical Systems,corresponding theories for the finite dimensional problems appear in a number of sources, as noted in the Commentary Section. Our emphasis here will be on the infinite dimensional theory, in the context of general nonlinear evolutionary equations. Most of the applications will be to the theory of so
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