Well-posedness of initial value problems for singular parabolic equations

We study well-posedness of initial value problems for a class of singular quasilinear parabolic equations in one space dimension. Simple conditions for wellposedness in the space of bounded nonnegative solutions are given, which involve boundedness of solutions of some related linear stationary problems. By a suitable change of unknown, the above results can be applied to classical initial-boundary value problems for parabolic equations with singular coefficients, as the heat equation with inverse square potential.