Partial Differential Equations: Approximate Solutions in Scales of Functional Spaces (Mathematical Research) - Hardcover

Gramchev, Todor V.; Popivanov, Petar R.

Hardcover

ISBN 10: 3527401385 ISBN 13: 9783527401383

Publisher: Wiley-VCH, 2000

Synopsis

The applications of methods from microlocal analysis for PDE have been a fast developing area during the last years. The authors, both are well known in the community, publish for the first time some of their research results in a summarized form. The essential point of the approach is the use of the various types of approximate (asymptotic) solutions in the study of differential equations in the smooth and the Gevrey spaces. In this volume, the authors deal with the following themes: Microlocal properties of pseudodifferential operators with multiple characteristics of involutive type in the framework of the Sobolev spaces; Abstract schemes for constructing approximate solutions to linear partial differential equations with characteristics of constant multiplicity m greater than or equal 2 in the framework of Gevrey spaces; Local solvability, hypoellipticity and singular solutions in Gevrey spaces; Global Gevrey solvability on the torus for linear partial differential equations; Applications of asymptotic methods for local (non)solvability for quasihomogeneous operators; Applications of Airy asymptotic solutions to degenerate oblique derivative problems for second order strictly hyperbolic equations; Approximate Gevrey normal forms of analytic involutions and analytic glancing hypersurfaces with applications for effective stability estimates for billiard ball maps.

About this title

Review

"...the authors are able to record the considerable progress realized recently in the field...topics have been chosen so that the reading is both attractive and useful, for experts and non-experts." (Mathematical Reviews Issue 2001g)

Edition details

• Publisher: Wiley-VCH
• Publication date: 2000
• ISBN 10: 3527401385
• ISBN 13: 9783527401383
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 155