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-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.