DSpace Collection:
http://www.openstarts.units.it:80/dspace/handle/10077/4098
2014-04-19T04:41:09ZCritical exponent for wave equation with potential
http://www.openstarts.units.it:80/dspace/handle/10077/4279
Title: Critical exponent for wave equation with potential
Authors: Georgiev, Vladimir; Heiming, Charlotte; Kubo, Hideo
Abstract: 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.
Type: Articolo2000-01-01T00:00:00ZSome new results on global nonexistence and blow-up for evolution problems with positive initial energy
http://www.openstarts.units.it:80/dspace/handle/10077/4278
Title: Some new results on global nonexistence and blow-up for evolution problems with positive initial energy
Authors: Vitillaro, Enzo
Abstract: 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.
Type: Articolo2000-01-01T00:00:00ZThe lifespan of classical solutions to systems of nonlinear wave equations
http://www.openstarts.units.it:80/dspace/handle/10077/4277
Title: The lifespan of classical solutions to systems of nonlinear wave equations
Authors: Takamura, Hiroyuki
Abstract: 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.
Type: Articolo2000-01-01T00:00:00ZFinite time blow-up for solutions of a hyperbolic system: the critical case
http://www.openstarts.units.it:80/dspace/handle/10077/4276
Title: Finite time blow-up for solutions of a hyperbolic system: the critical case
Authors: Pantarrotas, Atanasio
Abstract: 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.
Type: Articolo2000-01-01T00:00:00Z