Relation Between Solutions and Initial Values for Double-Nonlinear Diffusion Equation

作者：Deng, Liwei; Wang, Liangwei^*; Li, Min; Yin, Jingxue

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2022, 45(2): 939-952.

DOI：10.1007/s40840-021-01221-9

• Equivalence relation
• Asymptotic behavior
• omega-limit set
• Double-nonlinear diffusion equation

In this paper, we consider the Cauchy problem of the double-nonlinear diffusion equation. We establish the propagation speed estimates and space-time decay estimates for the solutions and study the equivalent relation between the solutions and the initial values. As an application of this relationship, we prove two different asymptotic behaviors for the solutions in the last of this paper.