Weak solutions of a nonlinear degenerate fourth‐order parabolic equation via the topological degree method

Abstract

In this paper, we study the existence of weak solutions for the nonlinear parabolic problem associated with the following fourth‐order equation, under Navier boundary conditions: where is a bounded domain. Under some appropriate assumptions, we obtain the existence of a weak solution for the above problem by using the topological degree theory for operators of the type , in the framework space .