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 well-posedness 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. (C) 2003 Elsevier Inc. All rights reserved.