Recently, research group of nonlinear hyperbolic partial differential equations leading by Prof. Wang Zhen made significant progress in the study of the Euler equations with damping and non-isentropic p-system with damping.

Prof. Wang Zhen and collaborators prove that any L∞ weak entropy solution to the Cauchy problem of damped Euler equations with finite initial mass converges strongly in the natural L1 topology with decay rates to the Barenblatt profile of the porous medium equation through a comprehensive entropy analysis. The density function tends to the Barenblatt solution of the porous medium equation while the momentum is described by Darcy’s law. The results have been accepted for publication by Arch. Rational Mech. Anal., the magazine is the top eight in the Journal of Mathematics, "Rank 8 of 74 in subject category Mathematics".

In addition, Prof. Wang Zhen and PhD. Geng Shifeng found optimal asymptotic state of non-isentropic p-system with damping and quasi-linear hyperbolic equation with damping, and obtain the optimal convergence rates through the comprehensive damping energy estimates. The results were accepted for publication by Communications in Partial Differential Equations and the Journal of Hyperbolic Differential Equations respectively.