TY  - GEN
AU  - Renardy, Michael
AU  - Rogers, Robert C.
TI  - An introduction to partial differential equations
T2  - Texts in applied mathematics
SN  - 0387979522 (acid-free paper)
AV  - QA374 .R42 2004
PY  - 2004///
CY  - New York
PB  - Springer
KW  - Diferansiyel denklemler, Kısmi
KW  - Differential equations, Partial
N1  - Includes bibliographical references and index; 1.Introduction --; 1.1.Basic Mathematical Questions --; 1.2.Elementary Partial Differential Equations --; 2.Characteristics --; 2.1.Classification and Characteristics --; 2.2.The Cauchy-Kovalevskaya Theorem --; 2.3.Holmgren's Uniqueness Theorem --; 3.Conservation Laws and Shocks --; 3.1.Systems in One Space Dimension --; 3.2.Basic Definitions and Hypotheses --; 3.3.Blowup of Smooth Solutions --; 3.4.Weak Solutions --; 3.5.Riemann Problems --; 3.6.Other Selection Criteria --; 4.Maximum Principles --; 4.1.Maximum Principles of Elliptic Problems --; 4.2.An Existence Proof for the Dirichlet Problem --; 4.3.Radial Symmetry --; 4.4.Maximum Principles for Parabolic Equations --; 5.Distributions --; 5.1.Test Functions and Distributions --; 5.2.Derivatives and Integrals --; 5.3.Convolutions and Fundamental Solutions --; 5.4.The Fourier Transform --; 5.5.Green's Functions --; 6.Function Spaces --; 6.1.Banach Spaces and Hilbert Spaces --; 6.2.Bases in Hilbert Spaces --; 6.3.Duality and Weak Convergence --; 6.4.Sobolev Spaces --; 7.Operator Theory --; 7.1.Basic Definitions and Examples --; 7.2.The Open Mapping Theorem --; 7.3.Spectrum and Resolvent --; 7.4.Symmetry and Self-adjointness --; 7.5.Compact Operators --; 7.6.Sturm-Liouville Boundary-Value Problems --; 7.7.The Fredholm Index --; 8.Linear Elliptic Equations --; 8.1.Definitions --; 8.2.Existence and Uniqueness of the Solutions of the Dirichlet Problem --; 8.3.Eigenfunction Expansions --; 8.4.General Linear Elliptic Problems --; 8.5.Interior Regularity --; 8.6.Boundary Regularity --; 9.Nonlinear Elliptic Equations --; 9.1.Perturbation Results --; 9.2.Nonlinear Variational Problems --; 9.3.Nonlinear Operator Theory Methods --; 10.Energy Methods for Evolution Problems --; 10.1.Parabolic Equations --; 10.2.Hyperbolic Evolution Problems --; 11.Semigroup Methods --; 11.1.Semigroups and Infinitesimal Generators --; 11.2.The Hille-Yosida Theorem --; 11.3.Applications to PDEs --; 11.4.Analytic Semigroups
ER  -