Adyghe Int. Sci. J. Vol. 22, No 2. P. 29-33. ISSN 1726-9946
|MSC 35L25||Original Article|
About one mixed problem for the inhomogeneous Hallaire equation
Ruzanna Khasanbievna Makaova
Junior Researcher of department Mixed type equations of Institute of Applied Mathematics and Automation of KBSC RAS (360017, 89 А Shortanova St., Nalchik, Russia), ORCID: https://orcid.org/ 0000-0003-4095-2332, email@example.com
Abstract. For the inhomogeneous Hallaire equation, a mixed boundary value problem is studied. The existence and uniqueness theorem for a regular solution is proved. An explicit form of the regular solution of the problem under study is written out.
Keywords: inhomogeneous Hallaire equation, mixed problem, regular solution, Fourier method
Acknowledgments: the author are thankful to the anonymous reviewer for his valuable remakes.
For citation. R. Kh. Makaova About one mixed problem for the inhomogeneous Hallaire equation. Adyghe Int. Sci. J. 2022. Vol. 22, No. 2. P. 29–33. DOI: https://doi.org/10.47928/1726-9946-2022-22-2-29-33
The author has read and approved the final version of the manuscript.
Submitted 24.06.2022; approved after reviewing 28.06.2022; accepted for publication 04.07.2022.
© Makaova R. Kh., 2022
1. M. Hallaire L’eau et la productions vegetable. Institut National de la Recherche Agronomique. 1964. Vol. 9.
2. A. M. Nakhushev Zadachi so smeshcheniem dlya uravnenij v chastnyh proizvodnyh [Problems with displacement for partial differential equations]. M.: Nauka, 2006. 287 p.
3. R. E. Showalter, T. W. Ting Pseudoparabolic partial differential equations. SIAM J. Math. Anal. 1970. Vol. 1, No. 1. P. 1–26.
4. D. Colton Pseudoparabolic Equations in One Space Variable. Journal of Differ. Equations. 1972. Vol. 12, no. 3. P. 559–565.
5. М. Kh. Shkhanukov Some boundary value problems for a third-order equation that arise in the modeling of the filtration of a fluid in porous media. Differ. Uravn. 1982. Vol. 18, No. 4. P. 689–699.
6. V. А. Vogahova A boundary value problem with A. M. Nakhushev’s nonlocal condition for a pseudoparabolic equation of moisture transfer. Differ. Uravn. 1982. Vol. 18, No. 18. P. 280–285.
7. R. Kh. Makaova The second boundary value problem for the generalized Hallaire equation with Riemann-Liouville fractional derivative. Reports AIAS. 2015. Vol. 17, No. 3. P. 35–38.
8. R. Kh. Makaova The first boundary value problem ib a nonlocal setting for the generalized Hallaire equation with Riemann-Liouville fractional derivative.
9. R. Kh. Makaova Mixed problem for the inhomogeneous Hallaire equation. Reports AIAS. 2021. Vol. 21, No. 4. P. 18–21.
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