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GCOE Seminars
Seminar information archive ～05/27｜Next seminar｜Future seminars 05/28～
2012/02/22
16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
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 R2, 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 R2, 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.
