Global existence of a classical solution for a large class of free boundary problems in one space dimension

We prove global classical solvability and a uniqueness theorem for a wide class of one dimensional free boundary problems in which the evolution of the free boundarys(t) is controlled by the derivatives up to the second order ofu (u together withs(t) is an unknown of our problem) and by a functional ofs(t) itself. In the Introduction it is showed the physical background from which such problems arise.Work partially supported by the Italian M.U.R.S.T. National Project Problemi non lineari...