Partial differential equations: time-periodic solutions - Otto Vejvoda
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Présentation Partial Differential Equations: Time - Periodic Solutions de Otto Vejvoda
- Livre Philosophie
Sommaire:
I Preliminaries from Functional Analysis.- ? 1. Linear Spaces and Operators.- ?2. Function Spaces.- ? 3. Existence Theorems for Operator Equations.- II Preliminaries from the Theory of Differential Equations.- ? 1. Boundary-Value and Eigenvalue Problems for Elliptic and Ordinary Differential Operators.- ? 2. The Wave and the Telegraph Equations.- ? 3. The Heat Equation.- III The Heat Equation.- ? 1. The (t, s)-Fourier Method.- ? 2. The t-Fourier and s-Fourier Methods.- ? 3. The Poincar? Method.- ? 4. Supplements and Comments on the Linear and Weakly Non-Linear Heat Equation.- ? 5. Comments on Strongly Non-Linear Parabolic Equations.- ? 6. Comments on the Navier-Stokes Equations and Related Problems.- IV The Telegraph Equation.- ? 1. The Fourier Methods.- ? 2. The Poincar? Method.- ? 3. Singularly Perturbed Problems.- ? 4. Supplements and Comments on Linear and Weakly Non-Linear Problems.- ? 5. Comments on Strongly Non-Linear Problems.- V The Wave Equation.- ? 1. The Dirichlet Boundary Conditions; the Poincar? Method.- ? 2. The Dirichlet boundary conditions; the G?nzlcr method.- ?3. Examples.- ? 4. The Newton and Combined Boundary Conditions; the G?nzler Method.- ? 5. Entrainment of Frequency.- ? 6. The Fourier Method.- ? 7. The Wave Equation in an Unbounded Domain.- ? 8. Supplements and Comments on Non-Autonomous Hyperbolic Equations.- ? 9. Comments on Autonomous Hyperbolic Equations.- VI The Beam Equation and Related Problems.- ? 1. The Equations of a Beam and of a Thin Plate.- ? 2. Supplements and Comments.- ? 3. The Dynamic von K?rm?n Equations of Thin Plates Involving Rotational Inertia and Damping.- VII The Abstract Equations.- ? 1. The t-Fourier method: Preliminaries.- ? 2. The t-Fourier Method: Spectral Properties of PeriodicOperators.- ? 3. The t-Fourier Method: Weakly Non-Linear Problems.- ? 4. Comments on Papers Using Direct Methods.- ? 5. Comments on Papers using Indirect Methods.- Bibliography to Chapter I.- Bibliography to Chapter II.- Bibliography to Chapter III.- Bibliography to Chapter IV.- Bibliography to Chapter V.- Bibliography to Chapter VI.- Bibliography to Chapter VII.- Bibliography of papers on related topics.- Addenda to bibliography.- List of Symbols.
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