## GCOE Seminars

Seminar information archive ～06/09｜Next seminar｜Future seminars 06/10～

### 2012/02/22

16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)

Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data. (ENGLISH)

**Oleg Emanouilov**(Colorado State University)Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data. (ENGLISH)

[ Abstract ]

In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.

Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data

$$

{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\\\\tilde Gamma}¥vert

- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}

$$

where $¥tilde ¥Gamma$ is an arbitrary fixed open set of

$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.

In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.

Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data

$$

{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\\\\tilde Gamma}¥vert

- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}

$$

where $¥tilde ¥Gamma$ is an arbitrary fixed open set of

$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.