5 papers
Regularity of Solutions to One-Dimensional Degenerate Diffusion Equations with Reactions
Bendong Lou, Junfan Lu
We study the one-dimensional reaction-diffusion equation \[ u_t=[A(u)]_{xx}+f(x,u). \] The diffusion operator belongs to a broad class of nonlinear degenerate diffusion operators t…
Dimension-Dependent Asymptotic Dynamics for Mean Curvature Flow with Robin Boundary Conditions
Xinfu Chen, Bendong Lou, Xiaoliu Wang +1
We consider a graphical mean curvature flow in a cylinder with Robin boundary conditions, which arises as a geometric model for interface motion in the singular limit of the Allen-…
Fife-McLeod's Theorem for Spatially Periodic Degenerate Diffusion Equations
Bendong Lou, Junfan Lu
For one dimensional homogeneous bistable diffusion equations, Fife-McLeod ([Arch. Ration. Mech. Anal., 65 (1977), 335-361]) gave a well-known theorem which says that spreading solu…
Asymptotic Behavior of Solutions of a Degenerate Diffusion Equation with a Multistable Reaction
Fang Li, Bendong Lou
We consider a generalized degenerate diffusion equation with a reaction term , where is a smooth function satisfying and $A(u),\ A'(u),\ A'…
Traveling Sharp Waves of Porous Media Equations in Spatially Periodic Environment
Bendong Lou
We consider one dimensional porous media equations in spatially periodic environment. We will construct a periodic traveling sharp wave whose profile tends to a positive steady sta…