A note on some inverse problems arising in lubrication theory. (English) Zbl 1224.35335

The authors formulate sufficient conditions on total forces to ensure the existence of a solution \((h,P)\) to the Reynolds equation which is used in lubrication theory. Here \(P\) is pressure and \(h\) represents the distance between two parallel planes. In the incompressible case, the unique solution has an explicit form involving the solution to the equation \(-\triangle w=1\) in \(\Omega \), \(w=0\) on \(\partial \Omega \). For compressible case the existence of a solution is proved only for a sufficiently small parameter which appears in the equation.


35Q35 PDEs in connection with fluid mechanics
35R30 Inverse problems for PDEs