Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors
Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors
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发表时间：
2001-04
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通讯作者：
James C. Robinson
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作者：
James C. Robinson
第一部分泛函分析：1.Banach和Hilbert空间2.常微分方程3.线性算子4.对偶空间5.Sobolev空间第二部分.存在唯一性理论：6.拉普拉斯7.线性抛物方程的弱解8.非线性反应扩散方程9.Navier-Stokes方程的存在唯一性第二部分.有限维整体吸引子：10.整体吸引子的存在和一般性质11.反应扩散方程的整体吸引子12.Navier-Stokes方程的整体吸引子13.有限维吸引子：理论与实例第三部分.有限维动力学：14.有限维动力学压缩性质：确定模式15.有限维动力学II，强压缩性质：惯性流形16.有限维动力学III，直接方法17.Kuramoto-Sivashinsky方程附录A.周期函数的Soblev空间附录B.使用体积元素的衰变来限制分维。
Part I. Functional Analysis: 1. Banach and Hilbert spaces 2. Ordinary differential equations 3. Linear operators 4. Dual spaces 5. Sobolev spaces Part II. Existence and Uniqueness Theory: 6. The Laplacian 7. Weak solutions of linear parabolic equations 8. Nonlinear reaction-diffusion equations 9. The Navier-Stokes equations existence and uniqueness Part II. Finite-Dimensional Global Attractors: 10. The global attractor existence and general properties 11. The global attractor for reaction-diffusion equations 12. The global attractor for the Navier-Stokes equations 13. Finite-dimensional attractors: theory and examples Part III. Finite-Dimensional Dynamics: 14. Finite-dimensional dynamics I, the squeezing property: determining modes 15. Finite-dimensional dynamics II, The stong squeezing property: inertial manifolds 16. Finite-dimensional dynamics III, a direct approach 17. The Kuramoto-Sivashinsky equation Appendix A. Sobolev spaces of periodic functions Appendix B. Bounding the fractal dimension using the decay of volume elements.