Existence and uniqueness of solutions for a class of semilinear parabolic PDEs with non-Lipschitz coefficients

In this paper the existence and uniqueness of solutions for a class of semilinear parabolic partial differential equations with non-Lipschitz coefficients on Riemannian manifold are obtained. Two non-Lipschitz functions are provided to show our results.  2005 Elsevier Inc. All rights reserved.