The Cauchy Problem
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.
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Chapter 0 Elements of Functional Analysis
The Abstract Cauchy Problem
Chapter 3 Dissipative Operators and Applications
Applications to Second Order Parabolic Equations
Chapter 5 Perturbation and Approximation of Abstract Differential Equations
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abstract Cauchy problem abstract differential equations adjoint Akad Amer Anal analytic applications approximation arbitrary argument assume assumptions Banach space belongs boundary value problems bounded operator C. R. Acad coefficients continuously differentiable convergence Corollary definition differential operators Dirichlet boundary condition dissipative operators Dokl domain duality map E D(A elliptic equations in Hilbert estimate evolution equations Example extension fact following result formula Fourier fractional powers G D(A hence Hilbert space holds hyperbolic implies inequality integral Lemma linear operators locally convex spaces m-dissipative Math Nauk SSSR nonlinear nonnegative norm obtain operator A0 parabolic equations partial differential equations perturbation Proc proof of Theorem propagator properly posed prove right-hand side Russian satisfies Schrodinger Section self-adjoint self-adjoint operator semi-groups of operators semigroups sense of distributions sequence strongly continuous subspace symmetric theory tions uniqueness Univ