In this work, we consider an initial problem for second order partial differential equations
with Caputo fractional derivatives in the time-variable and Bessel operator in the space …

We consider the massive Klein–Gordon equation on a class of asymptotically static
spacetimes (in the long-range sense) with Cauchy surface of bounded geometry. We prove …

The aim of this paper is to establish the H 1 global well-posedness for Kirchhoff systems.
The new approach to the construction of solutions is based on the asymptotic integrations for …

In this paper we consider weakly hyperbolic equations of higher orders in arbitrary
dimensions with time-dependent coefficients and lower order terms. We prove the Gevrey …

The goal of the present paper is to derive statements about energy estimates as well as L p−
L q decay estimates for a Klein–Gordon model with a particular time-dependent mass. The …

These notes provide an introduction to and a survey on recent results about the long-time
behaviour of solutions to systems of hyperbolic partial differential equations with time …

In this paper we analyse the Gevrey well-posedness of the Cauchy problem for weakly
hyperbolic equations of general form with time-dependent coefficients. The results involve …

arXiv:0711.0598v1 [math.AP] 5 Nov 2007 Page 1 arXiv:0711.0598v1 [math.AP] 5 Nov 2007
MULTIDIMENSIONAL DECAY IN VAN DER CORPUT LEMMA MICHAEL RUZHANSKY …

This paper describes an approach to global smoothing problems for non-dispersive
equations based on ideas of comparison principle and canonical transformation established …

In this note we provide dispersive estimates for Fourier integrals with parameter-dependent
phase functions in terms of geometric quantities of associated families of Fresnel surfaces …