### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

NOVEMBER 11, 2016

**Speaker: **
Svetlana Roudenko, George Washington University

**Title: ***
Heads and Tails in a Klein-Gordon equation
*

**Abstract:**
After the physicists Oskar Klein and Walter Gordon proposed in 1926 an equation that describes spinless relativistic electrons, the Klein-Gordon equation officially appeared in the quantum mechanics. On the other hand, one can view this model as a wave equation with a linear term added.

In this talk, I will discuss a nonlinear version of the Klein-Gordon equation in 3d, and explore its solutions that exist for all times vs the ones that may cease to exist in finite time. As it is related to the SchrÃ¶dinger equation, we can use tools of the dispersive equations machinery to investigate singularity formations or global in time behavior. In particular, the behavior near the ground or excited states produce various interesting solutions, and as we investigate further, interesting head and tails properties appear. I will compare the theoretical and numerical results in solution behavior for this equation and comment on extensions to other nonlinearities and extensions. Parts of this work is joint with Thomas Duyckaerts and also with Kai Yang and Yanxiang Zhao.

**Time:** Friday, November 11, 2016, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491