Overview

This volume focuses on recent developments in non-linear and hyperbolic equations. In the first contribution, the singularities of the solutions of several classes of non-linear partial differential equations are investigated. Applications concern the Monge-Ampere equation, quasi-linear systems arising in fluid mechanics as well as integro-differential equations for media with memory. There follows an article on L_p-L_q decay estimates for Klein-Gordon equations with time-dependent coefficients, explaining, in particular, the influence of the relation between the mass term and the wave propagation speed. The next paper addresses questions of local existence of solutions, blow-up criteria, and C^8 regularity for quasilinear weakly hyperbolic equations. Spectral theory of semibounded selfadjoint operators is the topic of a further contribution, providing upper and lower bounds for the bottom eigenvalue as well as an upper bound for the second eigenvalue in terms of capacitary estimates.

Full Product Details

Author:   Sergio Albeverio ,  Michael Demuth ,  Elmar Schrohe ,  Bert-Wolfgang Schulze
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2003 ed.
Volume:   145
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   1.040kg
ISBN:  

9783764321680

ISBN 10:   3764321687
Pages:   440
Publication Date:   24 October 2003
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Nonlinear PDE. Singularities, Propagation, Applications.- From Wave to Klein—Gordon Type Decay Rates.- Local Solutions to Quasi-linear Weakly Hyperbolic Differential Equations.- An Approach to a Version of the S(M, g)-pseudo-differential Calculus on Manifolds.- Spectral Invariance and Submultiplicativity for the Algebras of S(M, g)-pseudo-differential Operators on Manifolds.- Domain Perturbations and Capacity in General Hilbert Spaces and Applications to Spectral Theory.- An Interpolation Family between Gabor and Wavelet Transformations. Application to Differential Calculus and Construction of Anisotropic Banach Spaces.- Formes de torsion analytique et fibrations singulières.- Regularisation of Secondary Characteristic Classes and Unusual Index Formulas for Operator-valued Symbols.

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