Program
Nonlinear Hyperbolic Partial Differential Equations
Student No.:50
Time:Mon/Wed 13:00-14:50, 2015-05-13 ~ 2015-08-05(except for public holidays)
Instructor:Tao Luo  [City University of Hong Kong]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-5-13
Ending Date:2015-8-5
 

Description:

 

Nonlinear hyperbolic partial differential equations arise from many branches of sciences and engineering, such as fluid mechanics and general relativity. I will start with the basic notions such as characteristic manifolds, well-posedness and entropy, and end up with some current research topics such as free boundary problems of fluids interfaces and shock wave theory.. The emphasize will be on some important nonlinear systems such as compressible Euler equations and related Navier-Stokes equations.  Some typical methods such as weighted energy estimates, entropy estimates and constructions of nonlinear functionals will be discussed.

 

 

Prerequisite:

Basic theory of PDEs

 

 

Reference:

 

1. F. John, Partial Differenatial Equations. Springer-Verlag

2. A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Springer-Verlag.

3. C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag.

4. Tao Luo, Huihui Zeng. "Global Existence of Smooth Solutions and Convergence to Barenblatt Solutions for the Physical Vacuum Free Boundary Problem of Compressible Euler Equations with Damping ." Comm. Pure & Appl. Math. published online 2 FEB 2015 | DOI: 10.1002/cpa.21562 (2015). 

5. Tao Luo, Zhouping Xin & Huihui Zeng, On nonlinear asymptotic stability of Lane-Emden solutions for the viscous gaseous star problem, preprint 

6. Luo, T.; Xin, Z.; Zeng, H. Well-posedness for the motion of physical vacuum of the threedimensional compressible Euler equations with or without self-gravitation. Arch. Ration. Mech. Anal. 213 (2014), no. 3, 763–831.