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Matematicheskie Zametki, 2004, Volume 76, Issue 6, Pages 840–853
DOI: https://doi.org/10.4213/mzm156 (Mi mzm156) 		 
This article is cited in 64 scientific papers (total in 64 papers)

A Nonlinear Loaded Parabolic Equation and a Related Inverse Problem

A. I. Kozhanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (224 kB) Citations (64)
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DOI: https://doi.org/10.4213/mzm156
Abstract: The solvability of the nonlocal-in-time boundary-value problem for the nonlinear parabolic equation ut−Δu+c(u¯(x,T))u=f(x,t), where u¯(x,t)=α(t)u(x,t)+∫0tβ(τ)u(x,τ)dτ for given functions α(t) and β(t), is studied. Existence and uniqueness theorems for regular solutions are proved; it is shown that the results obtained can be used to study the solvability of coefficient inverse problems.
Received: 26.12.2001
English version:
Mathematical Notes, 2004, Volume 76, Issue 6, Pages 784–795
DOI: https://doi.org/10.1023/B:MATN.0000049678.16540.a5
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: A. I. Kozhanov, “A Nonlinear Loaded Parabolic Equation and a Related Inverse Problem”, Mat. Zametki, 76:6 (2004), 840–853; Math. Notes, 76:6 (2004), 784–795
Citation in format AMSBIB
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    • This publication is cited in the following 64 articles:
    1. Bazar Babajanov, Fakhriddin Abdikarimov, Alisher Babajonov, “The exact solitary and periodic wave solutions of the loaded nonlinear evolution equations via the functional variable method”, Boletim da Sociedade Paranaense de Matemática, 43 (2025)  crossref
    2. B. I. Islomov, D. A. Nasirova, “A problem with gellerstedt conditions on different characteristics for a mixed loaded equation of the second kind”, Eurasian Math. J., 15:1 (2024), 34–48  mathnet  crossref
    3. Guzel Ashurova, “Solvability of Coefficient Inverse Problems of Spatial Type for Parabolic Equations with Varying Involution Direction”, J Math Sci, 281:6 (2024), 837  crossref
    4. Minzilya Kosmakova, Danna Akhmanova, Kamila Izhanova, Kareem T. Elgindy, “BVP with a Load in the Form of a Fractional Integral”, International Journal of Mathematics and Mathematical Sciences, 2024 (2024), 1  crossref
    5. V. L. Kamynin, “Inverse problem of determining the absorption coefficient in a multidimensional nonuniformly parabolic equation”, Math. Notes, 116:5 (2024), 975–986  mathnet  crossref  crossref
    6. Kai Cao, “Identification of the time-dependent source term in a Kuramoto–Sivashinsky equation”, Journal of Inverse and Ill-posed Problems, 2023  crossref
    7. Hamed Ould Sidi, Mahmoud A. Zaky, Rob H. De Staelen, Ahmed S. Hendy, “Numerical Reconstruction of a Space-Dependent Reaction Coefficient and Initial Condition for a Multidimensional Wave Equation with Interior Degeneracy”, Mathematics, 11:14 (2023), 3186  crossref
    8. Kamil Basirovich Sabitov, Stanislav Nikolaevich Sidorov, “Inverse problems for equations of a mixed parabolic-hyperbolic type with power degeneration in finding the right-hand parts that depend on time”, Journal of Inverse and Ill-posed Problems, 31:6 (2023), 823  crossref
    9. Bazar Babajanov, Dilshod Atajonov, Odilbek Allaberganov, NOVEL TRENDS IN RHEOLOGY IX, 2997, NOVEL TRENDS IN RHEOLOGY IX, 2023, 020037  crossref
    10. Baltaeva U., Baltaeva I., Agarwal P., “Cauchy Problem For a High-Order Loaded Integro-Differential Equation”, Math. Meth. Appl. Sci., 45:13 (2022), 8115–8124  crossref  mathscinet  isi  scopus
    11. A. I. Kozhanov, R. R. Safiullova, “Ob odnom klasse psevdogiperbolicheskikh uravnenii s neizvestnym koeffitsientom”, Chelyab. fiz.-matem. zhurn., 7:2 (2022), 164–180  mathnet  crossref  mathscinet
    12. V. L. Kamynin, “Ob obratnoi zadache opredeleniya zavisyaschego ot prostranstvennoi peremennoi mladshego koeffitsienta v parabolicheskom uravnenii so slabym vyrozhdeniem”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii  i smezhnye problemy», Voronezh, 28 yanvarya – 2 fevralya 2021 g.  Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 206, VINITI RAN, M., 2022, 68–81  mathnet  crossref
    13. T. K. Yuldashev, E. T. Karimov, “Ob odnom nagruzhennom integro-differentsialnom uravnenii smeshannogo tipa s drobnymi operatorami Gerasimova—Kaputo”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 211, VINITI RAN, M., 2022, 96–113  mathnet  crossref
    14. B. I. Islomov, F. M. Juraev, “Local boundary value problems for a loaded equation of parabolic-hyperbolic type degenerating inside the domain”, Ufa Math. J., 14:1 (2022), 37–51  mathnet  crossref  mathscinet
    15. S. N. Sidorov, “Inverse Problems for a Three-Dimensional Equation of Parabolic-Hyperbolic Type in Finding Time-Dependent Factors of the Right-Hand Sides”, Lobachevskii J Math, 43:12 (2022), 3641  crossref
    16. Bazar Babajanov, Fakhriddin Abdikarimov, “Exact Solutions of the Nonlinear Loaded Benjamin-Ono Equation”, WSEAS TRANSACTIONS ON MATHEMATICS, 21 (2022), 666  crossref
    17. Bazar Babajanov, Fakhriddin Abdikarimov, “The Application of the Functional Variable Method for Solving the Loaded Non-linear Evaluation Equations”, Front. Appl. Math. Stat., 8 (2022)  crossref
    18. Kozhanov A.I., Shipina T.N., “Loaded Differential Equations and Linear Inverse Problems For Elliptic Equations”, Complex Var. Elliptic Equ., 66:6-7 (2021), 910–928  crossref  mathscinet  isi  scopus
    19. M. M. Sagdullaeva, “Nelokalnaya zadacha s integralnym usloviem dlya nagruzhennogo uravneniya teploprovodnosti”, Vestnik KRAUNTs. Fiz.-mat. nauki, 34:1 (2021), 47–56  mathnet  crossref
    20. B. I. Islomov, Y. K. Alikulov, “Analogues of the Cauchy-Goursat problem for a loaded third-order hyperbolic type equation in an infinite three-dimensional domain”, Sib. elektron. matem. izv., 18:1 (2021), 72–85  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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