Abstract:

       The large time behavior of the solutions to a multi-dimensional viscous conservation law is considered in this paper. It is shown that the solution time-asymptotically tends to the planar rarefaction wave if the initial perturbations are multi-dimensional periodic. The time-decay rate is also obtained. Moreover, a Gagliardo-Nirenberg type inequality is established in the domain RΧ Tⁿ, where Tⁿ is the n-dimensional torus. This is a joint work with Qian Yuan.

报告人简介：

   黄飞敏，现任中国科学院数学与系统科学研究院华罗庚首席研究员，国家自然科学基金杰出青年基金获得者。主要从事非线性偏微分方程的研究，在非线性双曲守恒律方程组解的适定性方面做出了重要贡献。2004年获美国工业与应用数学学会杰出论文奖(The SIAM Outstanding Paper Prize)，2013年获国家自然科学奖二等奖。