Generic singularities of solutions to a nonlinear wave equation.

Meeting Details

For more information about this meeting, contact Stephanie Geyer, Joseph Roberts, Yuxi Zheng.

Speaker: Alberto Bressan, Penn State

Abstract: The talk will be concerned with conservative solutions to the nonlinear wave equation u_{tt} - c(u)(c(u) u_x)_x = 0 For an open dense set of C^3 initial data, the conservative solution is piecewise smooth in the t - x plane, while the gradient u_x can blow up along finitely many characteristic curves. The analysis relies on a variable transformation which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem. A detailed description of the solution profile can be given, in a neighborhood of every singular point and every singular curve. Some results on structurally stable singularities have been obtained also for dissipative solutions. (This work is in collaboration with Geng Chen, Tao Huang, and Fang Yu).

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Room Reservation Information

Room Number: 216 McAllister

Date: 03/17/2015

Time: 10:00am - 11:00am