Parabolicity, Volterra Calculus, and Conical Singularities: A Volume of Advances in Partial Differential Equations: No. 138 (Operator Theory: Advances ... / Advances in Partial Differential Equations) - Hardcover

Hardcover

ISBN 10: 376436906X ISBN 13: 9783764369064

Publisher: Birkhauser Verlag AG, 2002

Synopsis

This volume highlights the analysis on noncompact and singular manifolds within the framework of the cone calculus with asymptotics. The three papers at the beginning deal with parabolic equations, a topic relevant for many applications. The first article presents a calculus for pseudodifferential operators with an anisotropic analytic parameter. The subsequent paper develops an algebra of Mellin operators on the infinite space-time cylinder. It is shown how timelike infinity can be treated as a conical singularity. In the third text - the central article of this volume - the authors use these results to obtain precise information on the long-time asymptotics of solutions to parabolic equations and to construct inverses within the calculus. There follows a factorization theorem for meromorphic symbols: it is proven that each of these can be decomposed into a holomorphic invertible part and a smoothing part containing all the meromorphic information. It is expected that this result will be important for applications in the analysis of nonlinear hyperbolic equations. The final article addresses the question of the coordinate invariance of the Mellin calculus with asymptotics.

Edition details

• Publisher: Birkhauser Verlag AG
• Publication date: 2002
• Language: English
• ISBN 10: 376436906X
• ISBN 13: 9783764369064
• Binding: Hardcover
• Number of pages: 367
• Editor: Albeverio Sergio, Demuth Michael, Schrohe Elmar, Schulze Bert-Wolfgang