Bu çalışmada eliptik denklem için Hadamard
anlamında kuvvetli kötü konulmuş olan bir ters problem ele alınmıştır. Bu
problemin çözümünün tekliği Carleman değerlendirmeleri yardımıyla
ispatlanmıştır.
[1]. Amirov, A. Kh., Integral Geometry and Inverse Problems for Kinetic Equations. Utrecht, The Netherlands: VSP, 2001.
[2]. Gölgeleyen, F. and Yamamoto, M., An inverse problem for the Vlasov–Poisson system. Journal of Inverse and Ill-posed Problems, 23-4 (2015) 363-372.
[3]. Gölgeleyen, I., An integral geometry problem along geodesics and a computational approach. An. Univ.“Ovidius” Constanţa, Ser. Mat, 18-2 (2010) 91-112.
[4]. Lavrent’ev, M. M., Some Improperly Posed Problems of Mathematical Physics. New York: Springer-Verlag, 1967.
[5]. Lavrent’ev, M. M., Romanov, V. G. and Shishatskii, S. P., Ill-Posed Problems of Mathematical Physics and Analysis. Providence: American Mathematical Society, 1986.
In this work, we consider an inverse problem for an elliptic equation
which is strongly ill-posed in Hadamard sense. We prove the uniqueness of the
solution of the problem by using Carleman estimates.
[1]. Amirov, A. Kh., Integral Geometry and Inverse Problems for Kinetic Equations. Utrecht, The Netherlands: VSP, 2001.
[2]. Gölgeleyen, F. and Yamamoto, M., An inverse problem for the Vlasov–Poisson system. Journal of Inverse and Ill-posed Problems, 23-4 (2015) 363-372.
[3]. Gölgeleyen, I., An integral geometry problem along geodesics and a computational approach. An. Univ.“Ovidius” Constanţa, Ser. Mat, 18-2 (2010) 91-112.
[4]. Lavrent’ev, M. M., Some Improperly Posed Problems of Mathematical Physics. New York: Springer-Verlag, 1967.
[5]. Lavrent’ev, M. M., Romanov, V. G. and Shishatskii, S. P., Ill-Posed Problems of Mathematical Physics and Analysis. Providence: American Mathematical Society, 1986.