摘要
In this paper,we are concerned with the asymptotic behavior of L^(∞) weak-entropy solutions to the compressible Euler equations with a vacuum and time-dependent damping-m/(1+t)^(λ).As λ∈(0,l/7],we prove tht the L^(∞) weak-entropy solution converges to the nonlinear diffusion wave of the generalized porous media equation(GPME)in L^(2)(R).As λ∈(1/7,1),we prove that the L^(∞) weak-entropy solution converges to an expansion around the nonlinear diffusion wave in L^(2)(R),which is the best asymptotic profile.The proof is based on intensive entropy analysis and an energy method.
作者
Shifeng GENG
Feimin HUANG
Xiaochun WU
耿世锋;黄飞敏;吴晓春(School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;School of Mathematics and Statistics,HNP-LAMA,Central South University,Changsha 410083,China)
基金
S.Geng's research was supported in part by the National Natural Science Foundation of China(12071397)
Excellent Youth Project of Hunan Education Department(21B0165)
F.Huang's research was supported in part by the National Key R&D Program of China 2021YFA1000800
the National Natural Science Foundation of China(12288201).
