Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (2000) s2

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https://www.openstarts.units.it/handle/10077/4098

CONTENTS

Rentaro Agemi
Global existence of nonlinear elastic waves

Philippe Clément and Stig-Olof Londen
Regularity aspects of fractional evolution equations

Ferruccio Colombini and Tatsuo Nishitani
On second order weakly hyperbolic equations and the Gevrey classes

P. D'Ancona, Vladimir Georgiev and Hideo Kubo
Weighted Strichartz estimate for the wave equation and low regularity solutions

Donatella Donatelli and Pierangelo Marcati
1-D Relaxation from Hyperbolic to Parabolic Systems with Variable Coefficients

Yury V. Egorov and Vladimir A. Kondratiev
On global solutions to a semilinear elliptic boundary problem in an unbounded domain

Vladimir Georgiev, Charlotte Heiming and Hideo Kubo
Critical exponent for wave equation with potential

Koji Kikuchi
Constructing weak solutions in a direct variational method and an application of varifold theory

Hideo Kubo and Masahito Ohta
Global existence and blow-up of the classical solutions to systems of semilinear wave equations in three space dimensions

Sandra Lucente and Guido Ziliotti
Global existence for a quasilinear Maxwell system

Albert Milani
Life-Span of solutions to nonlinear dissipative evolution equations: a singular perturbation approach

Atanasio Pantarrotas
Finite time blow-up for solutions of a hyperbolic system: the critical case

Hiroyuki Takamura
The lifespan of classical solutions to systems of nonlinear wave equations

Enzo Vitillaro
Some new results on global nonexistence and blow-up for evolution problems with positive initial energy

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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 14

Critical exponent for wave equation with potential
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Georgiev, Vladimir
;
Heiming, Charlotte
;
Kubo, Hideo
We establish a weighted L$^{\infty}$ estimate for the solution of the linear wave equation with a smooth positive potential depending only on space variables. This estimate is similar to F.John's estimates in $\left(\left[9\right]\right)$ and enables one to prove existence of global small data solution for the corresponding semilinear wave equation with potential.
916 417
Some new results on global nonexistence and blow-up for evolution problems with positive initial energy
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Vitillaro, Enzo
This paper deals with some new results on blow-up or global nonexistence for evolution equations with positive initial energy. The positive level of the energy which can be reached has a Mountain Pass type characterization, which is emphasized in the paper. We consider wave problems with source and damping in the interior or at the boundary of the domain and porous media equation with source, in both the slow diffusion and fast diffusion cases.
1130 641
The lifespan of classical solutions to systems of nonlinear wave equations
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Takamura, Hiroyuki
Any results in this talk are based on a joint paper with R. Agemi & Y. Kurokawa [1]. The existence of the critical curve for p-q systems of nonlinear wave equations was already established by D. Del Santo & V. Georgiev & E. Mitidieri [3] except for the critical case. Our main purpose is to prove a blow-up the orem for which the nonlinearity (p, q) is just on the critical curve in three space dimensions. Moreover, the lover and upper bounds of the lifespan of solutions are precisely estimated including the sub-critical case.
1101 435
Finite time blow-up for solutions of a hyperbolic system: the critical case
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Pantarrotas, Atanasio
It has already been proved that for the systems forming by m wave equations containing polynomial nonlinearities there exists a manifold that bounds the region of the blow-up in the half-space to which belong the parameters of nonlinearity. Here we prove the formation of singularities if the parameters belong to the critical manifold in three space dimensions.
845 531
Life-Span of solutions to nonlinear dissipative evolution equations: a singular perturbation approach
(Università degli Studi di Trieste. Dipartimento di Scienze Matematiche, 2000)
Milani, Albert
We investigate the large time behavior of solutions to nonlinear dissipative wave equations of the general form \[ \varepsilon u_{tt}+u_{t}-\Delta u=F\left(x,t,u,D_{x}u,D_{x}^{2}u\right); \] in particular, we study the dependence of the solutions $u=u^{\varepsilon}$ and of their life span $T_{\varepsilon}$ on the (small'' parameter $\varepsilon$. We are interested in the behavior of $u^{\varepsilon}$ and $T_{\varepsilon}$ as $\varepsilon\rightarrow0$, and in their relations with the solution v, and its life span T$_{p}$ , of the corresponding limit equation when $\varepsilon=0$, which is of parabolic type. We look for conditions under which either $T_{\varepsilon}=+\infty,\: or\: T_{\varepsilon}\rightarrow T_{p}\leq+\infty$ as $\varepsilon=0$.
673 445

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