Annotation 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.Heinz-Otto Kreiss, Jens Lorenz. At time t = 0 we give initial data (8.1.3) no.0) = to). and at the surfaces :cl = 0, :cl = l we prescribe linear (inhomogeneous) boundary conditions combining it and D, u. Introducing the notation y = (thaquot;-rx8)t we cananbsp;...
|Title||:||Initial-boundary Value Problems and the Navier-Stokes Equations|
|Author||:||Heinz-Otto Kreiss, Jens Lorenz|
|Publisher||:||SIAM - 1989|