Viscosity solutions of monotonic functional parabolic PDE (Q705110)

The paper deals with viscosity solutions of parabolic differential-functional equations \[ \partial _t u + f(t,x;u_t(\tau),u;D_xu, D_x^2 u) = 0, \quad (t,x) \in Q, \] \[ u(t,x) = 0, \quad (t,x) \in \Gamma, \] \[ u(t,x) = \phi(t,x), \quad t \in (-\overline{\tau},0), \;x \in \Omega, \] where \(u_t(\tau) = (u_t(\tau_1),\dots ,u_t(\tau_m))\), \(u_t(\tau_j) = u(t+\tau_j,x)\). Results for comparison, existence and uniqueness of solutions are proved and application is given to the retarded Bellman equation.