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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 748–760 (Mi mz4139)  

This article is cited in 12 scientific papers (total in 12 papers)

A Problem with a Nonlocal Boundary Condition on the Characteristic for a Class of Equations of Mixed Type

M. S. Salakhitdinova, M. Mirsaburovb

a Institute for Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan
b Termez State University

Abstract: We study the boundary-value problem with a nonlocal boundary condition on the characteristic for a class of equations of mixed type. The unique solvability of the problem is proved.

Keywords: differential equation of mixed type, TF problem, Cauchy problem, Hölder function, Carleman method, Wiener–Hopf equation, holomorphic function, residue theorem

DOI: https://doi.org/10.4213/mzm4139

Full text: PDF file (436 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2009, 86:5, 704–715

Bibliographic databases:

UDC: 517.956.6
Received: 17.08.2005
Revised: 20.02.2009

Citation: M. S. Salakhitdinov, M. Mirsaburov, “A Problem with a Nonlocal Boundary Condition on the Characteristic for a Class of Equations of Mixed Type”, Mat. Zametki, 86:5 (2009), 748–760; Math. Notes, 86:5 (2009), 704–715

Citation in format AMSBIB
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\paper A Problem with a Nonlocal Boundary Condition on the Characteristic for a Class of Equations of Mixed Type
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\vol 86
\issue 5
\pages 748--760
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\crossref{https://doi.org/10.1134/S0001434609110133}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Mirsaburov Mirakhmat, Khudzhaev Zhura, “Zadacha s usloviyami smescheniya na vnutrennikh kharakteristikakh i Franklya dlya uravneniya Gellerstedta s singulyarnym koeffitsientom”, Doklady Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 13:2 (2011), 41–42  elib
    2. M. Kh. Ruziev, “Problems with shifts for mixed elliptic-hyperbolic equations”, Russian Math. (Iz. VUZ), 56:1 (2012), 66–75  mathnet  crossref  mathscinet
    3. M. Kh. Ruziev, “A problem with the Frankl and Bitsadze–Samarskii condition on the line of degeneracy and on parallel characteristics for a mixed-type equation”, Russian Math. (Iz. VUZ), 56:8 (2012), 35–43  mathnet  crossref  mathscinet
    4. M. Kh. Ruziev, “On the Boundary-Value Problem for a Class of Equations of Mixed Type in an Unbounded Domai”, Math. Notes, 92:1 (2012), 70–78  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Mirsaburov M., Mirsaburova G.M., “On a problem with a shift and with the Frankl condition on a segment of the degeneration line for a class of equations of mixed type”, Differ. Equ., 48:3 (2012), 362–371  crossref  mathscinet  zmath  isi  elib  scopus
    6. M. Mirsaburov, Zh. Khudzhaev, “A problem with Tricomi and Frankl conditions on the characteristic for a class of mixed-type equations”, Russian Math. (Iz. VUZ), 57:1 (2013), 35–43  mathnet  crossref
    7. Gulbakhor M. Mirsaburova, “A mixed problem with Tricomi and Frankl conditions for the Gellerstedt equation with a singular coefficient”, Russian Math. (Iz. VUZ), 57:7 (2013), 13–26  mathnet  crossref
    8. Ruziev M.Kh., “Problem with Shifts in Interior Characteristics for Equations of Mixed Elliptic-Hyperbolic Type with a Singular Coefficient”, Differ. Equ., 49:8 (2013), 986–995  crossref  mathscinet  zmath  isi  scopus
    9. Mirsaburov M., Khudzhaev Zh.T., “Problem with Displacement Conditions on Internal Characteristics and the Frankl Condition on a Segment of the Degeneration Line for the Gellerstedt Equation with a Singular Coefficient”, Differ. Equ., 49:12 (2013), 1534–1543  crossref  mathscinet  zmath  isi  scopus
    10. G. M. Mirsaburova, “Bitsadze-Samarskii problem with a lacking shift condition for the Gellerstedt equation with a singular coefficient”, Differ. Equ., 50:5 (2014), 655–666  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    11. M. Mirsaburov, S. T. Chorieva, “Problem with shift on parallel characteristics for Gellerstedt equation with singular coefficient”, Russian Math. (Iz. VUZ), 61:5 (2017), 52–60  mathnet  crossref  isi
    12. M. Mirsaburov, “The problem with missing condition of shift for singular coefficiensy Gellerstedt equation”, Russian Math. (Iz. VUZ), 62:5 (2018), 44–54  mathnet  crossref  isi
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