PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yuxi Zheng, Tianyou Zhang.

Title:Uniqueness of conservative solutions to a variational wave equation
Seminar:Hyperbolic and Mixed Type PDEs Seminar
Speaker:Alberto Bressan, Penn State
Abstract:
An interesting class of variational wave equations take the form u_tt - c(u)(c(u)u_x)_x = 0, where c(u) > 0 is the wave speed. It is well known that solutions remain uniformly Holder continuous, but their gradient can blow up in finite time. When this happens, multiple solutions can be constructed. Uniqueness can be achieved by further imposing that the total energy remains constant in time. The uniqueness proof relies on a refined analysis of characteristics, which in this case satisfy an ODE with Holder continuous right hand side. The talk will present the main ideas in the construction, and review some earlier results on uniqueness for ODEs with possibly discontinuous right hand side.

Room Reservation Information

Room Number:MB216
Date:12 / 02 / 2014
Time:10:00am - 10:50am