Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations A Volume of Advances in Partial Differential Equations

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.Albeverio, Sergio is the author of 'Nonlinear Hyperbolic Equations, Spectral Theory, and Wavelet Transformations A Volume of Advances in Partial Differential Equations' with ISBN 9783764321680 and ISBN 3764321687.