Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds
نویسندگان
چکیده
In this work we derive local gradient and Laplacian estimates of the AronsonBénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman’s work we discover some new entropy formulae for these equations.
منابع مشابه
Gradient estimates for porous medium and fast diffusion equations via FBSDE approach
In this paper, we establish several gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques and Forward and Backward Stochastic Differential Equations (FBSDEs).
متن کاملA priori Lrho error estimates for Galerkin approximations to porous medium and fast diffusion equations
Galerkin approximations to solutions of a Cauchy-Dirichlet problem governed by the generalized porous medium equation
متن کاملA Priori L Error Estimates for Galerkin Approximations to Porous Medium and Fast Diffusion Equations
Galerkin approximations to solutions of a Cauchy-Dirichlet problem governed by the generalized porous medium equation
متن کاملEntropy-energy Inequalities and Improved Convergence Rates for Nonlinear Parabolic Equations
Abstract. In this paper, we prove new functional inequalities of Poincaré type on the one-dimensional torus S and explore their implications for the long-time asymptotics of periodic solutions of nonlinear singular or degenerate parabolic equations of second and fourth order. We generically prove a global algebraic decay of an entropy functional, faster than exponential for short times, and an ...
متن کاملLarge Time Behaviour of Solutions to Nonhomogeneous Diffusion Equations
This note is devoted to the study of the long time behaviour of solutions to the heat and the porous medium equations in the presence of an external source term, using entropy methods and self-similar variables. Intermediate asymptotics and convergence results are shown using interpolation inequalities, Gagliardo-Nirenberg-Sobolev inequalities and Csiszár-Kullback type estimates.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008