Classical solutions for a logarithmic fractional diffusion equation Articles uri icon

publication date

  • June 2014

start page

  • 901

end page

  • 924


  • 6


  • 101

International Standard Serial Number (ISSN)

  • 0021-7824

Electronic International Standard Serial Number (EISSN)

  • 1776-3371


  • We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion(1)∂tu+(-delta)1/2log(1+u)=0, posed for x∈R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C∞ smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.


  • logarithmic diffusion; nonlinear fractional diffusion; nonlocal diffusion operators; viscous transport equations