Sala Seminari (Dip. Matematica).
Large Data Solutions for Fractional Higher Order Nonlinear Equations. Abstract: We consider a class of evolution equation involving fractional Laplacian and nonlinear polynomial term. We discuss global existence in the energy space, decay estimates and self-similar asymptotic profile of the solutions provided that the nonlinear term is focusing. No requirement on the amplitude of the initial data is necessary and the order of the nonlinearity plays a weaker role with respect to the classical wave equation. This class includes wave equation with damping, beam equation with dissipative low oder term and can be interpreted as composition of diffusion equations.