Special Session 173: Mathematical and Numerical Analysis on Nonlinear PDEs

Asymptotic expansions of global solutions to the convection-diffusion equation with critical dissipation
Ryunosuke Kusaba
Tohoku University
Japan
Co-Author(s):    Taiki Takeuchi
Abstract:
This talk is concerned with the large-time behavior of global solutions to the Cauchy problem for the convection-diffusion equation with critical dissipation. The existence, decay estimates, and the first and second order asymptotic expansions of global solutions are established by using maximal regularity estimates in the homogeneous Besov spaces. In addition, with the aid of the self-similar structures in the asymptotic profiles, the optimal decay rates of the global solutions and the optimal convergence rates for the first order asymptotic expansion are determined.