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 Acad additional Akad Amer Anal Analysis analytic Appl applications approximation arbitrary argument assume assumptions Banach space belongs boundary condition bounded Cauchy problem closed compact complex consequence consider consists constant contained continuously differentiable convergence defined definition depend derivatives differential equations dissipative distributions Dokl domain easily element equality estimate evolution Example exists extension fact follows formula function given hand hence Hilbert space holds implies inequality initial integral Lemma limit linear Math means measure method Nauk SSSR nonlinear norm observe obtain obvious operator partial differential particular perturbation posed positive powers Proc proof propagator properties prove relation Remark respect result Russian satisfies Section self-adjoint semigroups sense sequence side similar solution strongly continuous sufficiently Theorem theory tions transform uniformly uniqueness Univ value problems write