Asymptotic analysis of a doubly nonlinear diffusion equation

作者：King J R^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2016, 138: 253-276.

DOI：10.1016/j.na.2015.12.003

• Nonlinear diffusion
• Moving boundary problems
• Image analysis

We investigate the doubly nonlinear diffusion equation
partial derivative u/partial derivative t = 1/n del.(u(m)vertical bar del u vertical bar(n-1)del u)
and the same equation expressed in terms of a 'pressure' variable. We classify various classes of compacted supported solutions, as well as finite-mass solutions that decay algebraically at infinity. A number of novel phenomena are identified, particularly for n < 0, that seem to us worthy of further mathematical investigation.

• 出版日期2016-6