The transient lubrication problem as a generalized Hele-Shaw type problem
The connection between the Hele-Shaw type problem and the lubrication problem is considered in this paper. The authors reformulate the first generalization of the Hele-Shaw problem as a time dependent variational inequality. To guarantee the equivalence between the strong and the weak formulation of the Hele-Shaw type problem, some new regularity results for the time dependent variational inequality of the first kind are established. The weak formulation for the lubrication problem with shear effects is deduced. In the case of the absence of shear effects, the uniqueness of the weak solution for the lubrication problem is obtained by a second abstract variational approach. Finally, the authors prove that the solution of the weak formulation of both Hele-Shaw type problems and shearless lubrication problems are the same, which means the Hele-Shaw phenomena can be regarded as a particular case of lubrication problem.
scientific article; zbMATH DE number 739094
scientific article