http://www.openstarts.units.it:80/dspace/handle/10077/4098 Sun, 19 May 2013 19:05:58 GMT 2013-05-19T19:05:58Z 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: Articolo Sat, 01 Jan 2000 00:00:00 GMT http://www.openstarts.units.it:80/dspace/handle/10077/4279 2000-01-01T00:00:00Z 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: Articolo Sat, 01 Jan 2000 00:00:00 GMT http://www.openstarts.units.it:80/dspace/handle/10077/4278 2000-01-01T00:00:00Z 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: Articolo Sat, 01 Jan 2000 00:00:00 GMT http://www.openstarts.units.it:80/dspace/handle/10077/4277 2000-01-01T00:00:00Z 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: Articolo Sat, 01 Jan 2000 00:00:00 GMT http://www.openstarts.units.it:80/dspace/handle/10077/4276 2000-01-01T00:00:00Z