Author | Dautray, Robert. author |
---|---|
Title | Mathematical Analysis and Numerical Methods for Science and Technology [electronic resource] : Volume 5 Evolution Problems I / by Robert Dautray, Jacques-Louis Lions |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2000 |
Connect to | http://dx.doi.org/10.1007/978-3-642-58090-1 |
Descript | XIV, 739 p. online resource |
XIV. Evolution Problems: Cauchy Problems in IRn -- ยง1. The Ordinary Cauchy Problems in Finite Dimensional Spaces -- ยง2. Diffusion Equations -- ยง3. Wave Equations -- ยง4. The Cauchy Problem for the Schrรถdinger Equation, Introduction -- ยง5. The Cauchy Problem for Evolution Equations Related to Convolution Products -- ยง6. An Abstract Cauchy Problem. Ovsyannikovโs Theorem -- Review of Chapter XIV -- XV. Evolution Problems: The Method of Diagonalisation -- ยง1. The Fourier Method or the Method of Diagonalisation -- ยง2. Variations. The Method of Diagonalisation for an Operator Having Continuous Spectrum -- ยง3. Examples of Application: The Diffusion Equation -- ยง4. The Wave Equation: Mathematical Examples and Examples of Application -- ยง5. The Schrรถdinger Equation -- ยง6. Application with an Operator Having a Continuous Spectrum: Example -- Review of Chapter XV -- Appendix. Return to the Problem of Vibrating Strings -- XVI. Evolution Problems: The Method of the Laplace Transform -- ยง1. Laplace Transform of Distributions -- ยง2. Laplace Transform of Vector-valued Distributions -- ยง3. Applications to First Order Evolution Problems -- ยง4. Evolution Problems of Second Order in t -- ยง5. Applications -- Review of Chapter XVI -- XVII. Evolution Problems: The Method of Semigroups -- A. Study of Semigroups -- ยง1. Definitions and Properties of Semigroups Acting in a Banach Space -- ยง2. The Infinitesimal Generator of a Semigroup -- ยง3. The HilleโYosida Theorem -- ยง4. The Case of Groups of Class &0 and Stoneโs Theorem -- ยง5. Differentiable Semigroups -- ยง6. Holomorphic Semigroups -- ยง7. Compact Semigroups -- B. Cauchy Problems and Semigroups -- ยง1. Cauchy Problems -- ยง2. Asymptotic Behaviour of Solutions as t ? + ?. Conservation and Dissipation in Evolution Equations -- ยง3. Semigroups and Diffusion Problems -- ยง4. Groups and Evolution Equations -- ยง5. Evolution Operators in Quantum Physics. The Liouvilleโvon Neumann Equation -- ยง6. Trotterโs Approximation Theorem -- Summary of Chapter XVII -- XVIII. Evolution Problems: Variational Methods -- Orientation -- ยง1. Some Elements of Functional Analysis -- ยง2. Galerkin Approximation of a Hilbert Space -- ยง3. Evolution Problems of First Order in t -- ยง4. Problems of First Order in t (Examples) -- ยง5. Evolution Problems of Second Order in t -- ยง6. Problems of Second Order in t. Examples -- ยง7. Other Types of Equation -- Review of Chapter XVIII -- Table of Notations -- of Volumes 1โ4, 6