(Ebook) Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations: A Volume of Advances in Partial Differential Equations by P. R. Popivanov (auth.), Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze (eds.) ISBN 9783034880732, 9783034894296, 3034880731, 3034894295

(Ebook) Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations: A Volume of Advances in Partial Differential Equations by P. R. Popivanov (auth.), Sergio Albeverio, Michael Demuth, Elmar Schrohe, Bert-Wolfgang Schulze (eds.) ISBN 9783034880732, 9783034894296, 3034880731, 3034894295

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.