HeinzOtto Kreiss and Jens Lorenz Classics in Applied Mathematics 47
InitialBoundary Value Problems and the NavierStokes Equations gives an introduction to the vast subject of initial and initialboundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The NavierStokes 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 InitialBoundary Value Problems and the NavierStokes Equations invaluable. The subjects addressed in the book, such as the wellposedness of initialboundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The book explains the principles of these subjects. The reader will learn what wellposedness or illposedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the NavierStokes equations.
When the book was written, the main intent was to write a text on initialboundary value problems that was accessible to a rather wide audience. Therefore, functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplications have been used throughout. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
Audience
This book continues to be useful to researchers and graduate students in applied math and engineering.
Contents
Preface to the Classics Edition; Errata; Introduction; Chapter 1: The NavierStokes Equations; Chapter 2: ConstantCoefficient Cauchy Problems; Chapter 3: Linear VariableCoefficient Cauchy Problems in 1D; Chapter 4: A Nonlinear Example: Burgers’ Equations; Chapter 5: Nonlinear Systems in One Space Dimension; Chapter 6: The Cauchy Problem for Systems in Several Dimensions; Chapter 7: InitialBoundary Value Problems in One Space Dimension; Chapter 8: InitialBoundary Value Problems in Several Space Dimensions; Chapter 9: The Incompressible NavierStokes Equations: The Spatially Periodic Case; Chapter 10: The Incompressible NavierStokes Equations under Initial and Boundary Conditions; Appendix 1: Notations and Results from Linear Algebra; Appendix 2: Interpolation; Appendix 3: Sobolev Inequalities; Appendix 4: Application of the ArzelaAscoil Theorem; References; Author Index; Subject Index.
2004 / xvii + 420 pages / Softcover / ISBN13: 9780898715651 / ISBN10: 0898715652 / List Price $60.50 / SIAM Member Price $42.35 / Order Code CL47
