Special Offers see all
More at Powell'sRecently Viewed clear list 
$12.95
New Trade Paper
Ships in 1 to 3 days
Available for Instore Pickup
in 7 to 12 days
Other titles in the Dover Books on Mathematics series:
Hilbert Space Methods in Partial Differential Equations (Dover Books on Mathematics)by Ralph E. Showalter
Synopses & ReviewsPublisher Comments:This text surveys the principal methods of solving partial differential equations. Suitable for graduate students of mathematics, engineering, and physical sciences, it requires knowledge of advanced calculus. The initial chapter contains an elementary presentation of Hilbert space theory that provides sufficient background for understanding the rest of the book. Succeeding chapters introduce distributions and Sobolev spaces and examine boundary value problems, first and secondorder evolution equations, implicit evolution equations, and topics related to optimization and approximation. The text, which features 40 examples and 200 exercises, concludes with suggested readings and a bibliography. Synopsis:This graduatelevel text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition. Synopsis:This graduatelevel text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition. Table of ContentsI. Elements of Hilbert Space Linear Algebra Convergence and Continuity Completeness Hilbert Space Dual Operators; Identifications Uniform Boundedness; Weak Compactness Expansion in Eigenfunctions II. Distributions and Sobolev Spaces Distributions Sobolev Spaces Trace Sobolev's Lemma and Imbedding Density and Compactness III. Boundary Value Problems Introduction Forms, Operators and Green's Formula Abstract Boundary Value Problems Examples Coercivity; Elliptic Forms Regularity Closed operators, adjoints and eigenfunction expansions IV. First Order Evolution Equations Introduction The Cauchy Problem Generation of Semigroups Accretive Operators; two examples Generation of Groups; a wave equation Analytic Semigroups Parabolic Equations V. Implicit Evolution Equations Introduction Regular Equations Pseudoparabolic Equations Degenerate Equations Examples VI. Second Order Evolution Equations Introduction Regular Equations Sobolev Equations Degenerate Equations Examples VII. Optimization and Approximation Topics Dirichlet's Principle Minimization of Convex Functions Variational Inequalities Optimal Control of Boundary Value Problems Approximation of Elliptic Problems Approximation of Evolution Equations What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
Other books you might likeRelated SubjectsScience and Mathematics » Mathematics » Differential Equations Science and Mathematics » Mathematics » General Science and Mathematics » Physics » General 

