Well-posedness and numerical approximation of a fractional diffusion equation with a nonlinear variable order
Abstract
We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with a variable fractional order that may depend on the unknown solution. We present a linearly implicit time-stepping method to linearize and discretize the equation in time, and present rigorous analysis for the convergence of numerical solutions based on proved regularity results.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2021
- Source ID
- 10.1051/m2an/2020072
Entities
People
- Buyang Li
- Hong Wang
- Jilu Wang
Organizations
- National Natural Science Foundation of China
- National Science Foundation