  The notes are an overview of part of the theory of pathwise weak solutions to
two classes of scalar fully nonlinear first- and second-order degenerate
parabolic partial differential equations with multiplicative rough time
dependence, a special case being Brownian. These are
Hamilton-Jacobi-Isaacs-Bellman and quasilinear divergence form equations
including multi-dimensional scalar conservation laws. If the time dependence is
`regular', the weak solutions are respectively the viscosity and
entropy/kinetic solutions. The results presented here are about the
wellposedness of the solutions. Some concrete applications are also discussed.
The material for the first class of problems are part of the ongoing
development of the theory in collaboration with P.-L. Lions.
