The Energy Method, Stability, and Nonlinear Convection
This book describes the energy method, a powerful technique for deriving nonlinear stability estimates in thermal convection contexts. It includes a very readable introduction to the subject (Chapters 2-4), which begins at an elementary level and explains
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Applied Mathematical Sciences 1. John: Partial Differential Equations, 4th ed. 2. Sirovich: Techniques of Asymptotic Analysis. 3. Hale: Theory of Functional Differential Equations, 2nd ed. 4. Percus: Combinatorial Methods. 5. von Mises/Friedrichs: Fluid Dynamics. 6. Freiberger!Grenander: A Short Course in Computational Probability and Statistics. 7. Pipkin: Lectures on Viscoelasticity Theory. 8. Giacaglia: Perturbation Methods in Non-linear Systems. 9. Friedrichs: Spectral Theory of Operators in Hilbert Space. 10. Stroud: Numerical Quadrature and Solution of Ordinary Differential Equations. II. Wolovich: Linear Multivariable Systems. 12. Berkovitz: Optimal Control Theory. 13. Bluman/Cole: Similarity Methods for Differential Equations. 14. Yoshizawa: Stability Theory and the Existence of Periodic Solution and Almost Periodic Solutions. 15. Braun: Differential Equations and Their Applications, 3rd ed. 16. Lefschetz: Applications of Algebraic Topology. 17. Col/atz/Wetterling: Optimization Problems. 18. Grenander: Pattern Synthesis: Lectures in Pattern Theory, Vol. I. 19. Marsden!McCracken: Hopf Bifurcation and Its Applications. 20. Driver: Ordinary and Delay Differential Equations. 21. Courant!Friedrichs: Supersonic Flow and Shock Waves. 22. Rouche/Habets!Laloy: Stability Theory by Liapunov's Direct Method. 23. Lamperti: Stochastic Processes: A Survey of the Mathematical Theory. 24. Grenander: Pattern Analysis: Lectures in Pattern Theory, Vol. II. 25. Davies: Integral Transforms and Their Applications, 2nd ed. 26. Kushner/Clark: Stochastic Approximation Methods for Constrained and Unconstrained Systems. 27. de Boor: A Practical Guide to Splines: Revised Edition. 28. Kei/son: Markov Chain Models-Rarity and Exponentiality. 29. de Veubeke: A Course in Elasticity. 30. Sniatycki: Geometric Quantization and Quantum Mechanics. 31. Reid: Sturmian Theory for Ordinary Differential Equations. 32. Meis/Markowitz: Numerical Solution of Partial Differential Equations.
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Grenander: Regular Structures: Lectures in Pattern Theory, Vol. III. Kevorkian!Cole: Perturbation Methods in Applied Mathematics. Carr: Applications of Centre Manifold Theory. Bengtsson/Ghil/Kiillen: Dynamic Meteorology: Data Assimilation Methods. Saperstone: Semidynamical Systems in Infinite Dimensional Spaces. Lichtenberg/Lieberman: Regular and Chaotic Dynamics, 2nd ed. Piccini!Stampacchia!Vidossich: Ordinary Differential Equations in R•. Naylor/Sell: Linear Operator Theory in Engineering and Science. Sparrow: The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Guckenheimer/Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Ockendon!Taylor: Inviscid Fluid Flows. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Glashoff!Gustafson: Linear Operations and Approximation: An Introduction to the Theoretical Analysis and Numerical Treat
