Nonexplosion and solvability of nonlinear diffusion equations on noncompact manifolds - Antoniouk, A.Val.; Antoniouk, A.Vict. (Український математичний журнал, 2007)
We find sufficient conditions on coefficients of diffusion equation on noncompact manifold, that guarantee non-explosion of solutions in a finite time. This property leads to the existence and uniqueness of solutions for corresponding stochastic differential equation with globally non-Lipschitz coefficients.