Conditions for the Existence of Global Solutions to Doubly Nonlinear Advection-diffusion Equations

In this work, we consider a initial-value problem for an doubly non linear advection-diffusion equation, and we present a critical value of κ up to wich the initial-value problem has global solution independent of the initial data u0, and from which global solutions may still exists, but from initial data u0 satisfying certain conditions. For this, we suppose that the function f(x,t,u) in the advection term, writted in the divergent form, satisfies certain conditions about your variation in Rn, and we also use the decrease of the norm L1(Rn) and an control for the norm L∞(Rn) of solution u(·,t).