The initial boundary value problem of the nonlinear parabolic conical degenerate p−Laplacian operator is considered in this paper. Our first step was to prove the generalized conical Hardy inequality and the embedding result for conical Sobolev spaces on a manifold with conical singularity.We then showed the global existence of a weak solution. We investigated its asymptotic behavior using potential well theory. Finally,we obtained the blow-up property in finite time for the solution of the nonlinear parabolic conical degenerate Laplacian problem with singular potential and sourceweighted functions.
