SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2491-2522, January 2021.
We rigorously show the nonequilibrium-diffusion limit of the compressible Euler-P1 approximation model arising in radiation hydrodynamics as the Mach number tends to zero when the initial data is well prepared. In particular, the effect of the large temperature variation upon the limit is taken into account. The model leads to a singular problem which fails to fall into the category of the classical theory of singular limits for quasi-linear hyperbolic equations. By introducing an appropriate normed space of solutions and exploiting the structure of the system, we establish the uniform local existence of smooth solutions and the convergence of the model to the incompressible nonhomogeneous Euler system coupled with a diffusion equation.

中文翻译：

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低马赫数下可压缩Euler-P1近似辐射模型的非平衡扩散极限

SIAM数学分析杂志，第53卷，第2期，第2491-2522页，2021年1月。
我们严格地显示了辐射流体动力学中可压缩的Euler-P1近似模型的非平衡扩散极限，因为当准备好初始数据时，马赫数趋于零。尤其要考虑温度变化大对极限的影响。该模型导致了一个奇异问题，该问题未能落入准线性双曲型方程奇异极限经典理论的范畴。通过引入适当的规范化解空间并利用系统的结构，我们建立了光滑解的统一局部存在性，并将模型收敛到了带有扩散方程的不可压缩非齐次Euler系统。