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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bubbling and extinction for some fast diffusion equations in bounded domains
有界域 快速扩散方程 气泡 消光
2023/11/13
Motivated by the Wisconsin octupole experiments on anomalous diffusion of hydrogen plasma across a purely poloidal octupole magnetic field, Berryman-Holland 1980 proved the stability of separable solu...
Generic fast diffusion for a class of non-convex Hamiltonians with two degrees of freedom
fast diffusion non-convex Hamiltonians two degrees of freedom
2015/9/25
In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees offreedom, and we prove a result of diffusion for an open and dense set of perturbations, ...
Gradient estimates for porous medium and fast diffusion equations via FBSDE approach
Gradient estimates porous medium fast diffusion equations FBSDE approach Probability
2012/6/27
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 t...
Total Variation Flow and Sign Fast Diffusion in one dimension
Fast Diffusion Total Variation Flow asymptotic extinction profile convergence rates extinction time
2011/9/1
Abstract: We consider the dynamics of the Total Variation Flow (TVF) $u_t=\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE) $u_t=\Delta\sign(u)$ in one spatial dimension. We find the expli...
Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption
Very singular solution singular diffusion gradient absorption self-similar solutions p-Laplacian uniqueness
2011/8/26
Abstract: Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption {equation*} \partial_t u -\Delta_{...
Behaviour near extinction for the Fast Diffusion Equation on bounded domains
Nonlinear evolution singular parabolic fast di usion Harnack asymptotics
2011/1/18
We consider the Fast Di usion Equation ut = um posed in a bounded smooth domain
Rd with homogeneous Dirichlet conditions; the exponent range is ms = (d 2)+=(d + 2) < m < 1.It is known...
Convergence of the Dirichlet solutions of the very fast diffusion equation
very fast diffusion equation Dirichlet problem
2011/2/21
For any −1 < m < 0, μ > 0, 0 ≤ u0 ∈ L∞(R) such that u0(x) ≤ (μ0|m||x|) 1 m for any |x| ≥ R0 and some constants R0 > 1 and 0 < μ0 ≤ μ, and f, g ∈C([0,∞)) such that f(t), g(t) ≥ μ0 on [0,∞) we pro...