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This article studies the nonequilibrium–diffusion limit of the compressible Euler model arising in radiation hydrodynamics in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$ with the general initial data. Combining the moment method with Hilbert expansion, we show that the radiative intensity can be approximated by the sum of interior solution and initial layer. We also show that the solution satisfied by the density, temperature, and velocity can be approximated by the interior solutions. Our results can be considered as an extension from 핋3 in arXiv.2312.15208 by Ju, Li, and Zhang to ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$. In contrast to arXiv.2312.15208, we get the exact convergence rates by studying the error system derived from the primitive system, the zeroth‐order to the second‐order about the radiative intensity, and the zeroth‐order about the hydrodynamics. [ABSTRACT FROM AUTHOR]

In this paper, we consider a free boundary tumor model with a periodic supply of external nutrients, so that the nutrient concentration σ satisfies σ = ϕ(t) on the boundary, where ϕ(t) is a positive periodic function with period T. A parameter μ in the model is proportional to the "aggressiveness" of the tumor. If 0<σ˜ 0 with respect to all radially symmetric perturbations. We prove that under nonradially symmetric perturbations, there exists a number μ∗ such that if 0 < μ < μ∗, then the T‐periodic solution is linearly stable, whereas if μ > μ∗, then the T‐periodic solution is linearly unstable. [ABSTRACT FROM AUTHOR]