Blow-up for Nonlinear Hyperbolic Problems

"By using the concept of nonlinear capacity we suggest the general approach to the blow-up phenomena in nonlinear problems. This approach does not use the maximum principle arguments and properties of the fundamental solutions of related differential operators. That fact gives the possibility to consider a wide classes of nonlinear problems and obtain the sharp results for blow-up problems including the estimates for the ""blow-up time"". Finally we construct the ""Mendeleev table"" for nolinear problems. I am going to demonstrate this approach for nonlinear (multidimensional) hyperbolic problems. The results are obtained jointly with E.Mitidieri, L.Veron and A.Tesei."