Reconstruction of Potential Function for Diffusion Operator

Abstract

Inverse spectral problem for diffusion operator consists in reconstruction of this operator by its spectrums and norming constants. In this paper, we are concerned with inverse problem for diffusion operator using a new kind of spectral data that is known as nodal points. We give a reconstruction of q as a limit of a sequence of functions whose nth term is dependent only eigenvalue and its associated nodal data. The technique we use to obtain the results is an adaptation of the method discussed in the reference Chen et al

Stability of inverse nodal problem for energy-dependent sturm liouville equation

“…Lemma 2.5. [27] The solutions of the problems (1.1)-(1.3) and (1.1),(1.3),(2.11) have the following forms,…”

“…Inverse nodal problem for diffusion operator is to determine potential functions and parameters in the boundary conditions. This type problems have been studied by many authors [27], [28], [29], [30], [31].…”

Sınır Koşulunda Öz Parametre Bulunduran Bir Sturm-Liouville Operatörü İçin Ters Nodal Problem

“…Daha sonra, bazı yazarlar tarafından dikkate değer bazı sonuçlar elde edilmiştir. Örneğin, bazı yazarlar çalışmalarında nodal noktalar yardımıyla potansiyel fonksiyonu ve türevlerini yeniden yapılandırmıştır (Chen vd., 2002;Koyunbakan ve Panakhov, 2007;Koyunbakan ve Yılmaz, 2008;Koyunbakan, 2009Koyunbakan, , 2011Yang, 2014;Pinasco ve Scarola, 2015). Bu çalışmalara ek olarak bazı yazarlar sınır koşullarının öz parametreye bağlı olması durumunda ters nodal problemi ele aldılar (Browne ve Sleeman, 1996;Yılmaz ve Koyunbakan, 2010;Panakhov vd., 2010;Keskin ve Özkan, 2017;Şen, 2017, 2018.…”

An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions

“…Some aspects of this type problems were studied by many authors (see [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]). Such problems play an important role in mathematics and have many applications in natural sciences and engineering.…”