Synopses & Reviews
This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
Synopsis
This book gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs.
Table of Contents
Preface to the Classics Edition; Introduction; 1. The Navier-Stokes equations; 2. Constant-coefficient Cauchy problems; 3. Linear variable-coefficient Cauchy problems in 1D; 4. A nonlinear example: Burgers' equations; 5. Nonlinear systems in one space dimension; 6. The Cauchy problem for systems in several dimensions; 7. Initial-boundary value problems in one space dimension; 8. Initial-boundary value problems in several space dimensions; 9. The incompressible Navier-Stokes equations: the spatially periodic case; 10. The incompressible Navier-Stokes equations under initial and boundary conditions; Appendices; References; Author index; Subject index.