| 000 | 02364 a2200241 4500 | ||
|---|---|---|---|
| 008 | 240328b |||||||| |||| 00| 0 eng d | ||
| 020 | _a9780521635646 | ||
| 082 | _a514.74 ROB | ||
| 100 | _aRobinson, James C. | ||
| 245 | _aInfinite-dimensional dynamical systems: an introduction to dissipative parabolic PDEs and the theory of global attractors | ||
| 260 |
_aCambridge: _bCambridge University Press, _c2001. |
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| 300 |
_axvii, 461p.: _bpbk.: _c23cm. |
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| 440 | _aCambridge Texts in Applied Mathematics | ||
| 504 | _aIncludes References and Index | ||
| 520 | _aThis book develops the theory of global attractors for a class of parabolic PDEs which includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systems of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves 'finite-dimensional'. The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral. Develops theory of PDEs as dynamical systems, theory of global attractors, and some consequences of that theory Only a low level of previous knowledge of functional analysis is assumed, so accessible to the widest possible mathematical audience Numerous exercises, with full solutions available on the web https://www.cambridge.org/in/universitypress/subjects/mathematics/differential-and-integral-equations-dynamical-systems-and-co/infinite-dimensional-dynamical-systems-introduction-dissipative-parabolic-pdes-and-theory-global-attractors?format=PB | ||
| 650 | _aDissipative Parabolic PDEs | ||
| 650 | _aNavier-Stokes Equations | ||
| 650 | _aBanach and Hilbert Spaces | ||
| 650 | _aKuramoto-Sivashinsky Equation | ||
| 650 | _aLaplacian | ||
| 650 | _aSobolev Spaces | ||
| 942 |
_cTD _2ddc |
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| 999 |
_c60101 _d60101 |
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