Equações de evolução com laplaciano fracionário: existência, unicidade, estimativas Lp-Lq, conservação generalizada de energia e espalhamento

Abstract

In this thesis we study some sigma-evolution equations in the Petrowsky's sense. When the coefficients are constant we obtain Lp-Lq estimates for linear equations and apply them to obtain results of existence, uniqueness and Blow-up for a semilinear model. When we have time-dependent coefficients, we obtain Lp-Lq estimates, energy estimates and scattering for linear problems.