Xiao-Jing Xu

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

This paper establishes the global existence of non-negative weak solutions to a two-dimensional, fourth-order nonlinear degenerate parabolic equation modeling surface-tension-driven convection in thin fluid films. First, we construct a regularized approximate problem and prove its solvability via the Galerkin method. U...