Asymptotic Properties of Solutions to the Cauchy Problem for Degenerate Parabolic Equations with Inhomogeneous Density on Manifolds

Abstract We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. give a qualitative classification of behavior solutions depending function at infinity and geometry manifold, which is described in terms its isoperimetric function. establish properties as: stabilization solution to zero large times, finite speed propagation, universal bounds solution, blow up interface. Each one these behaviors course takes place suitable range parameters, whose definition involves geometrical characteristic function, both manifold asymptotics infinity.