##### Department of Mathematics,

University of California San Diego

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### Computational and Applied Mathematics Seminar

## Hailiang Liu

#### Department of Mathematics, Iowa State University

## Computing Multi-valued Solutions for Euler-Poisson Equations

##### Abstract:

In this talk we first review the critical threshold phenomena for Euler-Poisson equations, which arise in the semiclassical approximation of Schrodinger-Poisson equations and plasma dynamics. We then present a phased space-based level set method for the computation of multi-valued velocity and electric fields of one-dimensional Euler-Poisson equations. This method uses an implicit Eulerian formulation in an extended space, which incorporates both velocity and electric fields into the configuration space. Multi-valued velocity and electric fields are captured through common zeros of two level set functions, which solve a linear homogeneous transport equation in the field space. The superposition principle for multi-valued solutions is established.

Host: Philip Gill

### March 13, 2007

### 11:00 AM

### AP&M 7321

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