## EVENT DETAILS AND ABSTRACT

**PDE Seminar**
**Title:** A Nonlinear Variational Wave Equation

**Speaker:** Professor Yuxi Zheng

**Speaker Info:** Indiana University-Bloomington

**Brief Description:**

**Special Note**: **SPECIAL TIME**

**Abstract:**

A nonlinear wave equation arises in a simplified liquid crystal model through
the variational principle. The wave speed of the wave equation is a given
function of the wave amplitude. It has been known for the equation that
smooth initial data may develop singularities in finite time, a sequence
of weak solutions may develop concentrations, while oscillations may persist.
We formulate a viscous approximation of the equation and establish the
global existence of smooth solutions for the viscously perturbed equation.
For monotone wave speed functions in the equation, we find an invariant
region in the phase space in which we discover:
(a) smooth data evolve smoothly forever;
(b) both the viscous regularization and the smooth solutions obtained
through data mollification and step (a) for not-as-smooth initial data
yield weak solutions to the Cauchy problem of the nonlinear variational
wave equation. The main tool is the Young measure theory and related
techniques.

**Date:** Thursday, March 18, 1999

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Gui-Qiang Chen

**Contact email:** gqchen@math.nwu.edu

**Contact Phone:** 847-491-5553

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