Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations
Subtitle: a Volume of Advances in Partial Differential Equations
By: edited by Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze
Contributors: Demuth, Michael; Schrohe, Elmar; Schulze, Bert-Wolfgang
Series: Operator Theory: Advances and Applications -- 145; Operator theory, advances and applications -- 145.
Publisher: Birkhäuser Basel; Imprint; Birkhäuser
Published: 2003
Place of publication: Basel
Language: eng
Format: [electronic resource] :
Number of pages: 437
ISBN-13: 9783034880732
Subjects: Functional analysis; Mathematics; Differential equations, partial; Mathematical physics; Operator theory
Description: 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-Ampère 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.