2021/11/22 by Nangao Zhang, Zhang, Nangao, Changjiang Zhu +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2111.11035
openalex publication_date 2021/11/22 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/01
In this paper, we are concerned with the asymptotic behavior of solutions of M1 model proposed in the radiative transfer fields. Starting from this model, combined with the compressible Euler equation with damping, we introduce a more general system. We rigorously prove that the solutions to the Cauchy problem of this system globally exist and time-asymptotically converge to the shifted nonlinear diffusion waves whose profile is self-similar solution to the corresponding parabolic equation governed by the classical Darcy's law. Moreover, the optimal convergence rates are also obtained. Compared with previous results obtained by Nishihara, Wang and Yang in [29], we have a weaker and more general condition on the initial data, and the conclusions are more sharper. The approach adopted in the paper is the technical time-weighted energy estimates with the Green function method together.