Ricerc@Sapienza

We consider the Cauchy problem (Equation Presented) where - is a network and H is a positive homogeneous Hamiltonian which may change from edge to edge. In the first part of the paper, we prove that the Hopf-Lax type formula gives the (unique) viscosity solution of the problem. In the latter part of the paper we study a ame propagation model in a network and an optimal strategy to block a fire breaking up in some part of a pipeline; some numerical simulations are provided.

Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $??(0, 1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices.

We prove that the only symplectic semifield spreads of PG(5,q^2), q>= 2^14, even, whose associated semifield has center containing F_q, is the Desarguesian spread, by proving that the only F_q-linear set of rank 6 disjoint from the secant variety of the Veronese surface of PG(5,q^2) is a plane with three points of the Veronese surface PG(5,q^6)\PG(5,q^2).