## Seminar:

Fall 2010, Thursdays, Milner 216, 4:00-4:50 PM
__ Date:__ ** September 16 **

**" Finding the Discontinuity Point of the Potential of Sturm-Liouville Problem by Inverse spectral Method "**

**Kun Gou**

__Abstract__The direct Sturm-Liouville problem(SLP) is introduced first. This equals to find the spectrum more mathematically called egeinvalues, given the partial differential equation of SLP. Thoererical analsysi and properties are presented for this one. Then we have a look at how we construct the inverse SLP. The inverse spectral problem equals finding the potential of the SLP given the spectrum. The mumercial realization for the partially known potential type is demonstrated for the inverse problem. Then we are given a Sturm-Liouville problem, the potential of which has one discontinuity point. And the only unkonw for the potential is the positon of the discontinuity. Under this condition, we show how we find the discontinuity by the partially known potential type. At the end, we analyze a fatal disease called atherosclerosis of human being. We apply our inverse spectral problem of finding discontinuity of potential to this medical engineering model and see how it helps solve this medical difficulty.