http://www.openstarts.units.it:80/dspace/handle/10077/3919 2013-05-18T15:49:23Z http://www.openstarts.units.it:80/dspace/handle/10077/3931 Title: Fundamental Solutions for Hyperbolic Operators with Variable Coefficients Authors: Yagdjian, Karen Abstract: In this article we describe a new method to construct fundamental solutions for operators with variable coefficients. That method was introduced in {\it J. Differential Equations} {\bf 206} (2004), 227-252, to study the Tricomi-type equation. More precisely, the new integral operator is suggested which transforms the family of the fundamental solutions of the Cauchy problem for the equation with the constant coefficients to the fundamental solutions for the operators with variable coefficients. Type: Article 2010-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/3930 Title: Energy Inequalities and Dispersive Estimates for Wave Equations with Time-Dependent Coefficients Authors: Wirth, Jens Abstract: We consider wave models with lower order terms and survey some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is complemented by a collection of open problems. Type: Article 2010-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/3929 Title: An Elementary Hilbert Space Approach to Evolutionary Partial Differential Equations Authors: Picard, Rainer Abstract: The purpose of this paper is to provide a survey of an approach to evolutionary problems originally developed in {\it Int. J. Pure Appl. Math.} {\bf 50}, No. 2, (2009) 283-288, and {\it Math. Methods Appl. Sci.} {\bf 32}, No. 14, (2009) 1768-1803, for a special case. The ideas are extended to a much larger problem class and the utility of the approach is exemplified by a Robin type initial boundary value problem for acoustic waves. The paper concludes with an outlook to open directions of further research. Type: Article 2010-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/3928 Title: On Wave Equations with Dissipation II Authors: Nakazawa, Hideo Abstract: Our recent results on wave equations with dissipation are surveyed and resolvent estimates for stationary dissipative wave equations in an exterior domain are also proved. Type: Article 2010-01-01T00:00:00Z