Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.42 (2010) s.

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https://www.openstarts.units.it/handle/10077/3919

CONTENTS

Francesco Colombini and Ferruccio Fanelli
A Note on Nonhomogeneous Hyperbolic Operators with Low Regularity Coefficients

Anahit Galstian
L^p- L^q-Decay Estimates for the Klein-Gordon Equation in the Anti-de Sitter Space-Time

Vladimir Georgiev, Jmmy Alfonso Mauro and George Venkov
Spectral Properties of an Operator Associated with Hartree Type Equations with External Coulomb Potential

Marina Ghisi and Massimo Gobbino
Hyperbolic-Parabolic Singular Perturbation for Kirchhoff Equations with Weak Dissipation.

Marina Ghisi and Massimo Gobbino
Kirchhoff Equations in Generalized Gevrey Spaces: Local Existence, Global Existence, Uniqueness

Hideo Kubo and Matoharu Takaki
A Remark on Long Range Effect for a System of Semilinear Wave Equations

Tokio Matsuyama
The Kirchhoff Equation with Global Solutions in Unbounded Domains

Kiyoshi Mochizuki
Resolvent Estimates for Magnetic Schrödinger Operators and Their Applications to Related Evolution Equations

Hideo Nakazawa
On Wave Equations with Dissipation II

Rainer Picard
An Elementary Hilbert Space Approach to Evolutionary Partial Differential Equations

Jens Wirth
Energy Inequalities and Dispersive Estimates for Wave Equations with Time-Dependent Coefficients

Karen Yagdjian
Fundamental Solutions for Hyperbolic Operators with Variable Coefficients

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Editorial policy The journal Rendiconti dell’Istituto di Matematica dell’università di Trieste publishes original articles in all areas of mathematics. Special regard is given to research papers, but attractive expository papers may also be considered for publication. The journal usually appears in one issue per year. Additional issues may however be published. In particular, the Managing Editors may consider the publication of supplementary volumes related to some special events, like conferences, workshops, and advanced schools. All submitted papers will be refereed. Manuscripts are accepted for review with the understanding that the work has not been published before and is not under consideration for publication elsewhere. Our journal can be obtained by exchange agreements with other similar journals.

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Now showing 1 - 5 of 12

Fundamental Solutions for Hyperbolic Operators with Variable Coefficients
(EUT Edizioni Università di Trieste, 2010)
Yagdjian, Karen
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.
1232 906
Energy Inequalities and Dispersive Estimates for Wave Equations with Time-Dependent Coefficients
(EUT Edizioni Università di Trieste, 2010)
Wirth, Jens
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.
1007 700
An Elementary Hilbert Space Approach to Evolutionary Partial Differential Equations
(EUT Edizioni Università di Trieste, 2010)
Picard, Rainer
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.
912 810
On Wave Equations with Dissipation II
(EUT Edizioni Università di Trieste, 2010)
Nakazawa, Hideo
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.
1166 962
Resolvent Estimates for Magnetic Schr\"odinger Operators and Their Applications to Related Evolution Equations
(EUT Edizioni Università di Trieste, 2010)
Mochizuki, Kiyoshi
In this article we survey some basic results for the magnetic Schr\"odinger operator with external potential which has a strong singularity. The following topics are treated under suitable decay conditions on the magnetic field and external potential: Selfadjointness of the operator, Growth estimates of generalized eigenfunctions, Principle of limiting absorption, Uniform resolvent estimates, and Smoothing properties for corresponding evolution equations.
1207 724

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