Periodic solutions of a nonlinear propagation equation via a fixed point argument

In this work the initial value problem for the equation $$u_t + beta u_x + yf(u)_x - delta u_{xxt} = g,forall x in R, forall t in [0,T],$$ with periodic boundary conditions is interpreted in the sense of periodic distributions and studied via fixed point arguments. Weak solutions exist iff∈C ⁰ (R) andg∈L ^∞(L ²(0,1)). Moreover, regularity inf, g and the initial data implies regularity of solutions.