A half-inverse problem for singular diffusion operator with certain boundary conditions

ERGÜN A., AMİROV R.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, cilt.38, sa.4, ss.916-927, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1002/num.22713
  • Dergi Adı: NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.916-927
  • Anahtar Kelimeler: inverse spectral problems, spectrum, Sturm&#8211, Liouville operator, uniqueness, STURM-LIOUVILLE OPERATORS, SPECTRAL PROBLEMS
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

In this paper, we studied the half inverse spectral problem for singular diffusion operator with certain boundary conditions. The discontinuity function in this operator is defined as delta(x)=1,x is an element of(0a1)alpha 2,x is an element of(a1a2)beta 2,x is an element of(a2 pi) and alpha > 0, alpha not equal 1, beta > 0, beta not equal 1 and a(1), a(2) is an element of (0, pi), a1 is an element of 0 pi 2, a2 is an element of pi 2 pi. We prove that the potential functions p(x) and q(x) are determined uniquely by using the Yang-Zettl and Hocstadt-Lieberman methods. We examine that if potential functions q(x) and p(x) are prescribed over the interval pi 2 pi, then reconstruction of the potential functions q(x) and p(x) by one spectrum on the (0, pi).