The Cauchy ProblemCambridge University Press, 1983 - 636 pages This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students. |
Table des matières
Chapter 0 Elements of Functional Analysis | 1 |
The Abstract Cauchy Problem | 26 |
General Theory | 62 |
Chapter 3 Dissipative Operators and Applications | 117 |
Applications to Second Order Parabolic Equations | 172 |
Chapter 5 Perturbation and Approximation of Abstract Differential Equations | 267 |
Chapter 6 Some Improperly Posed Cauchy Problems | 346 |
Chapter 7 The Abstract Cauchy Problem for TimeDependent Equations | 381 |
Chapter 8 The Cauchy Problem in the Sense of VectorValued Distributions | 461 |
References | 510 |
627 | |
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Expressions et termes fréquents
abstract Cauchy problem abstract differential equations adjoint Akad Amer Anal analytic Appl applications approximation arbitrary argument assume assumptions Au(t B₁ Banach space belongs boundary value problems bounded operator C. R. Acad coefficients continuously differentiable convergence Corollary definition Differencial'nye Uravnenija differential operators Dirichlet boundary condition dissipative dissipative operators Dokl domain duality map E)-valued elliptic equations in Hilbert estimate evolution equations Example extension fact formula fractional powers hence Hilbert space holds implies inequality integral L²(R Lemma linear operators m-dissipative Math Nauk SSSR nonlinear nonnegative norm obtain parabolic equations partial differential equations perturbation Proc proof of Theorem propagator properly posed prove Russian satisfies Schrödinger Section self-adjoint self-adjoint operator semi-groups of operators semigroups sequence solution strongly continuous subset subspace theory tions u₁ uniqueness Univ