Decay property of regularity-loss type for nonlinear hyperbolic-elliptic system in multi-dimensions

作者：Wang, Wenjun^*

来源：Journal of Mathematical Analysis and Applications, 2012, 387(2): 993-1008.

DOI：10.1016/j.jmaa.2011.10.013

• Hyperbolic-elliptic system
• Regularity-loss
• Green function
• Multi-dimensions
• Time-weight energy estimate

this paper, we study the asymptotic behavior of solutions for a hyperbolic-elliptic system with a 2m-order elliptic part in multi-dimensional space. This system is a modified version of the simplest radiating gas model and it verifies L-p decay property of regularity-loss type in R-n. The global existence and L-p estimates of the solution to the Cauchy problem for the hyperbolic-elliptic system are obtained. Since the dissipative property of this system is so weak in high frequency region, the usual energy method does not work well in deriving the a priori estimates for global solutions to the nonlinear problem. Our analysis is based on a frequency decomposition and the method of combining the Green function with some time-weight energy estimates.

• 出版日期2012-3-15
• 单位上海理工大学