Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

1st Edition

Victor A. Galaktionov, Enzo L. Mitidieri, Stanislav I. Pohozaev

Chapman and Hall/CRC
Published September 22, 2014
Reference - 569 Pages - 178 B/W Illustrations
ISBN 9781482251722 - CAT# K23839
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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Summary

Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger 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.