DIRECT AND INVERSE PROBLEMS FOR DIFFUSION OPERATOR WITH DISCONTINUITY POINTS

Temel Bulgular & Veri:Under certain initial and jump conditions, integral equations have been derived for solutions and integral representation have been presented.

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Sonuç & Katkı:Reconstruction of the diffusion operator with discontinuity points problem have been proved by Weyl function, spectral datas and two sectra.

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:Alan Parametreleri

Özet

In this study, the diffusion operator with discontinuity points has been considered. Under certain initial and jump conditions, integral equations have been derived for solutions and integral representation have been presented. Some important spectral properties of eigenvalue and eigenfunctions have been obtained. Reconstruction of the diffusion operator with discontinuity points problem have been proved by Weyl function, spectral datas and two sectra.

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Bu Makaleye Atıf Yap

ERGÜN, A., AMİROV, R. (2019). DIRECT AND INVERSE PROBLEMS FOR DIFFUSION OPERATOR WITH DISCONTINUITY POINTS. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 9 - Sayı: 1, 9–21. https://ajindex.com/articles/341351

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Kaynakça (14)

Marchenko, V. A., (1986), Sturm-Liouville Operators and Applications, AMS Chelsea Publishing, Basel
Levitan, B. M. and Gasymov, M. G., (1964), Determination of a differential equation by two spectra. Uspekhi Mathematicheskikh Nauk, 19, 2, 3-63
Jaulent, M. and Jean, C., (1976), The Inverse Problem for the one-dimensional Schr¨odinger equation with an energy-dependent potential. Annales de L’Institut Henri Poincare A, 25, 2, 105-137
Yurko, V. A., (2000), Introduction to the Theory of Inverse Spectral Problems, Fizmatlit, MOscow, Russia, 2007, English translation, Inverse Spectral Problems dor Differantial Operators and Their Applications, Gordon and Breach, Amsterdam, The Netherlands
Levitan, B. M., (1978), Inverse Sturm-Liouville Problems, Nauka, Moscow, Russia
Gasymov M. G. and Guseinov, G. S., (1981), Determination of a diffusion operator from spectral data, Akademiya Nauk Azerbaidzhanskoi SSR. Doklady, 37, 2, 19-23
Yurko, V. A., (2000), An inverse problem for differential operator pencils, Methematicheskikh Sbornik, 191, 10, 137-160
Nabiev, M. I., (2004), The inverse spectral problem for he diffusion operator on an interval. Mathematicheskaya Fizika, Analiz, Geometriya, 11, 3, 302-313, [9] Guseinov, G. S., (1986), Inverse spectral problems for a quadratic pencil of Sturm-Liouville operators on a finite interval. Spectral Theory of Operators and Its Applications, 51-101, Elm, Baku, Azerbaijan
Freiling G. and Yurko V., (2001), Inverse Sturm-Liouville problems and their applications, Nova Science, Huntington, NY, USA
Yurko, V. A., (2000), Inverse spectral problems for differential operators and their applications, vol. 2 of Analytical Methods and Special Functions, Gordon and Breach, Amsterdam, The Netherlands [12] Hald, O. H., (1984), Discontinuous inverse eigenvalue problems, Communications on Pure and Applied Mathematics, 37, 5, 539–577
Amirov, R. Kh., (2006), On Sturm-Liouville operators with discontinuity conditions inside an interval.Journal of Mathematical Analysis and Applications, 317, 1, 163-176
AmirovR. Kh. and Yurko, V. A., (2001), On differential operators with a singularity and discontinuity conditions inside an interval.Ukrainian Mathematical Journal, 53,11,1443–1457
FreilingG.and Yurko, V., (2002), Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point. Inverse Problems, 18, 3, 757-773
Levin, B. Ya., (1