The initial value problem for a nonlinear nonuniform parabolic equation (Q1109964)

The initial value problem for a nonlinear nonuniformly parabolic equation is studied. The coefficient of the nonlinear term is defined by the operator \((-\Delta)^{\alpha /2}\) with \(\alpha\in (0,n)\). The goal is to prove the global existence of a smooth solution for any smooth initial data. Conditions which guarantee the above results are given. They involve the parameter \(\alpha\) and the dimension n.