Abstract:
For a fourth-order equation with two independent variables a variant of the Goursat problem with data on two intersecting characteristics is considered. It includes not only the construction of the desired function, but also the coefficients of the equation. Thus, we are talking about the inverse problem of determining the coefficients of the equation. The method of construction of conditions providing allocation of infinite number of sets of this type equations is offered, for which the problem under consideration is solvable in quadratures. Instead of introducing additional boundary conditions, restrictions on the structure of the equation are proposed, related to the possibilities of its factorization.
\Bibitem{Zhe19}
\by V.~I.~Zhegalov
\paper On a proplem for generalized Boussinesq--Love equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2019
\vol 23
\issue 4
\pages 771--776
\mathnet{http://mi.mathnet.ru/vsgtu1720}
\crossref{https://doi.org/10.14498/vsgtu1720}
Linking options:
https://www.mathnet.ru/eng/vsgtu1720
https://www.mathnet.ru/eng/vsgtu/v223/i4/p771
This publication is cited in the following 4 articles:
Sh. Karimov, Sh. Oripov, “A Cauchy Problem for the Boussinesq–Love Equation with the Bessel Operator”, Lobachevskii J Math, 45:9 (2024), 4520
A. V. Gilev, L. S. Pulkina, “Two Problems for Fourth Order Equations with Nonlocal Conditions in Characteristic Domain”, J Math Sci, 270:4 (2023), 547
A. V. Bogatov, A. V. Gilev, L. S. Pulkina, “Zadacha s nelokalnym usloviem dlya uravneniya chetvertogo poryadka s kratnymi kharakteristikami”, Vestnik rossiiskikh universitetov. Matematika, 27:139 (2022), 214–230
A. V. Gilev, O. M. Kechina, L. S. Pulkina, “Kharakteristicheskaya zadacha dlya uravneniya chetvertogo poryadka s dominiruyuschei proizvodnoi”, Vestn. SamU. Estestvennonauchn. ser., 27:3 (2021), 14–21
Citation in format AMSBIB
Contact us: