L P decay for general hyperbolic-parabolic systems of balance laws
L P decay for general hyperbolic-parabolic systems of balance laws
复制标题
一般双曲-抛物线平衡定律系统的 L P 衰减
DOI：
10.3934/dcds.2018018
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发表时间：
2017
影响因子：
1.1
通讯作者：
Yanni Zeng
中科院分区：
文献类型：
--
作者：
Yanni Zeng
研究了多维空间中一般双曲-抛物平衡律方程组解的时间渐近衰减性。该系统具有物理粘度矩阵和用于松弛、阻尼或化学反应的低阶项。低阶项的粘性矩阵和雅可比矩阵是亏秩的。对于常平衡点附近的Cauchy问题，在一组合理的假设下，最近建立了整体时间解的存在性。本文给出了当p≥2时的最优L^p衰减率.我们的结果是普遍的，并适用于物理模型，如气体流动的平移和振动的非平衡。我们的结果也恢复或改进了文献中关于双曲-抛物守恒律和双曲平衡律的特殊情形的已有结果。
We study time asymptotic decay of solutions for a general system of hyperbolic-parabolic balance laws in multi space dimensions. The system has physical viscosity matrices and a lower order term for relaxation, damping or chemical reaction. The viscosity matrices and the Jacobian matrix of the lower order term are rank deficient. For Cauchy problem around a constant equilibrium state, existence of solution global in time has been established recently under a set of reasonable assumptions. In this paper we obtain optimal $L^p$ decay rates for $p≥2$. Our result is general and applies to physical models such as gas flows with translational and vibrational non-equilibrium. Our result also recovers or improves the existing results in literature on the special cases of hyperbolic-parabolic conservation laws and hyperbolic balance laws, respectively.