Some problems of parabolic type with discontinuous nonlinearities on convex constraints (Q917794)

The author considers the semilinear equation of parabolic type \[ \partial u/\partial t=\Delta u+g(u),\quad \Omega \times (0,\infty);\quad u=0,\quad \partial \Omega \times (0,\infty) \] with a discontinuous nonlinearity g, and also associated inequalities with convex or nonconvex constraints \(u\geq \phi\), \(\int_{\Omega}u^ 2 dx=\rho^ 2\). Generalizing the notion of the subdifferential of a convex function the author obtains the solutions as curves of maximal relaxed slope for an appropriate functional corresponding to the given constraint.