The abstract results apply to a large variety of problems. Thus, the well-known Benjamin-Bona-Mahony-Burgers equation and Rosenau-Burgers equations with sources and many other physical problems are considered as examples. Moreover, the method proposed for studying blow-up phenomena for nonlinear Sobolev-type equations is applied to equations which play an important role in physics. For instance, several examples describe different electrical breakdown mechanisms in crystal semiconductors, as well as the breakdown in the presence of sources of free charges in a self-consistent electric field.
The monograph contains a vast list of references (440 items) and gives an overall view of the contemporary state-of-the-art of the mathematical modeling of various important problems arising in physics. Since the list of references contains many papers which have been published previously only in Russian research journals, it may also serve as a guide to the Russian literature.
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.
The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.
Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
The Green Crawler is one of the coolest superheroes around, and Frank and Joe are some of his biggest fans. And thanks to a contest, the Hardy boys get to be two of the handlers for the new Green Crawler balloon in the annual Fall Festival parade in Bayport!
But the day before the parade, disaster strikes: someone has ripped the Green Crawler balloon! The people in charge think Joe did it—and the Hardys need to clear his name fast. Was it Bayport bully Adam Ackerman, who was green with envy that the Hardys won the contest? Or could the culprits be loyal fans of Nutty the Squirrel, the cartoon character whom the Green Crawler replaced? And Mo Mantis, the Green Crawler’s archenemy, has a few tricks of his own…
Can the brothers figure out who tried to ground the Green Crawler? Or will Joe and Frank be watching the parade from the sidelines this year?
With his influential “counternovel” HOPSCOTCH and his unforgettable short stories, Cortázar earned a place among the most innovative authors of the twentieth century. HOPSCOTCH is a nonlinear novel about an Argentinean writer living in Paris; it consists of 155 short chapters that the author advises the reader to read out of order. BLOW-UP and WE LOVE GLENDA SO MUCH bring together the most famous of Cortázar’s short fiction, including “Axolotl,” “End of the Game,” “The Night Face Up,” “Continuity of Parks,” “Bestiary,” and “Blow-Up”. These are stories in which invisible beasts stalk children in their homes, the reader of a mystery finds out that he is the murderer’s intended victim, an injured motorcyclist is pursued by Aztec warriors, and a man becomes a salamander in a Parisian zoo. In Cortázar’s work, laws of nature, physics, and narrative fall away, leaving us with an astonishing new view of the world.
(Book Jacket Status: Jacketed)