Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schroedinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.
The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking common features. The book describes many properties of the equations and examines traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities.
Preparing readers for more advanced mathematical PDE analysis, the book demonstrates that quasilinear degenerate higher-order PDEs, even exotic and awkward ones, are not as daunting as they first appear. It also illustrates the deep features shared by several types of nonlinear PDEs and encourages readers to develop further this unifying PDE approach from other viewpoints.
- ISBN10 1482251728
- ISBN13 9781482251722
- Publish Date 22 September 2014 (first published 1 January 2014)
- Publish Status Active
- Publish Country CA
- Imprint Apple Academic Press Inc.
- Format Hardcover
- Pages 569
- Language English