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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 1, Pages 99–110 (Mi zvmmf55)  

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

A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation

I. G. Mamedov

Institute of Cybernetics, National Academy of Sciences of Azerbaijan, ul. F. Agaeva 9, Baku, AZ1141, Azerbaijan

Abstract: The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a $\theta$-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem.

Key words: fourth-order pseudoparabolic equation, Cauchy problem, equations with discontinuous coefficients, fundamental solution.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:1, 93–104

Bibliographic databases:

UDC: 519.63
Received: 21.01.2008

Citation: I. G. Mamedov, “A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 99–110; Comput. Math. Math. Phys., 49:1 (2009), 93–104

Citation in format AMSBIB
\by I.~G.~Mamedov
\paper A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 1
\pages 99--110
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 1
\pages 93--104

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. G. Mamedov, “Ob odnoi trekhmernoi zadache Gursa novogo tipa dlya giperbolicheskogo uravneniya s razryvnymi koeffitsientami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(20) (2010), 209–213  mathnet  crossref
    2. I. G. Mamedov, “One Goursat problem in a Sobolev space”, Russian Math. (Iz. VUZ), 55:2 (2011), 46–55  mathnet  crossref  mathscinet
    3. I. G. Mamedov, “Formula integrirovaniya po chastyam neklassicheskogo tipa pri issledovanii zadachi Gursa dlya odnogo psevdoparabolicheskogo uravneniya”, Vladikavk. matem. zhurn., 13:4 (2011), 40–51  mathnet
    4. Mamedov I., “Neumann Problem in the Non-Classical Treatment for a Fourth Order Pseudoparabolic Equation”, 2012 IV International Conference Problems of Cybernetics and Informatics (Pci), ed. AidaZade K., IEEE, 2012  isi
    5. I. G. Mamedov, “Nonclassical Analog of the Goursat Problem for a Three-Dimensional Equation with Highest Derivative”, Math. Notes, 96:2 (2014), 239–247  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Mamedov I.G., “On a Nonclassical Interpretation of the Dirichlet Problem For a Fourth-Order Pseudoparabolic Equation”, Differ. Equ., 50:3 (2014), 415–418  crossref  mathscinet  zmath  isi  elib  scopus
    7. I. G. Mamedov, “Nelokalnaya kombinirovannaya zadacha tipa Bitsadze–Samarskogo i Samarskogo–Ionkina dlya sistemy psevdoparabolicheskikh uravnenii”, Vladikavk. matem. zhurn., 16:1 (2014), 30–41  mathnet
    8. I. G. Mamedov, “O neklassicheskoi traktovke chetyrekhmernoi zadachi Gursa dlya odnogo giperbolicheskogo uravneniya”, Vladikavk. matem. zhurn., 17:4 (2015), 59–66  mathnet
    9. Mamedov I.G., “on the Well-Posed Solvability of the Dirichlet Problem For a Generalized Mangeron Equation With Nonsmooth Coefficients”, Differ. Equ., 51:6 (2015), 745–754  crossref  mathscinet  zmath  isi  elib  scopus
    10. A. T. Assanova, Zh. S. Tokmurzin, “An Approach to the Solution of the Initial Boundary-Value Problem for Systems of Fourth-Order Hyperbolic Equations”, Math. Notes, 108:1 (2020), 3–14  mathnet  crossref  crossref  mathscinet  isi  elib
    11. A. T. Assanova, Z. S. Tokmurzin, “A nonlocal multipoint problem for a system of fourth-order partial differential equations”, Eurasian Math. J., 11:3 (2020), 8–20  mathnet  crossref
    12. A. N. Mironov, L. B. Mironova, Yu. O. Yakovleva, “Metod Rimana dlya uravnenii s dominiruyuschei chastnoi proizvodnoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 25:2 (2021), 207–240  mathnet  crossref  zmath
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