Weak solutions to an initial-boundary value problem for a model of convection driven by surface tension

This paper is concerned with weak solutions to an initial -boundary value problem for a fourth order nonlinear degenerate parabolic equation, which is used to simulate the convection phenomenon dominated by the surfacetension -driven mechanism. First, we construct a modified problem of the initial -boundary value problem. Then, constructing an energy functional with special form and using the energy method, we obtain the uniform a -priori estimates of the solutions to the modified problem. Next, the Aubin-lions lemma is used to take the limit of the solutions to get the weak solutions to an approximate problem of the initial -boundary value problem. Finally, introducing the special integral functions, we prove the non -negativity of the solutions and obtain the global existence of weak solutions to the initial -boundary value problem.