Mixed Boundary Value Problem for a Monotone Equation with a Lower Order Term and Point Sources on the Right Side
https://doi.org/10.26907/2541-7746.2024.2.173-186
Abstract
The existence of a solution to the mixed boundary value problem for a quasilinear equation with a lower order term and point sources on the right side was proved. The solution was obtained in an additive form, and the features associated with point sources were clearly highlighted. The approach used in the proof can serve as a basis for a method of solving this type of problem.
About the Authors
O. А. Zadvornov
Kazan Federal University
Russian Federation
Russian Federation
Kazan, 420008
G. O. Trifonova
Kazan Federal University
Russian Federation
Russian Federation
Kazan, 420008
References
1. Barenblatt G.I., Entov V.M., Ryzhik V.M. Dvizhenie zhidkostei i gazov v prirodnykh plastakh [The Motion of Fluids and Gases in Natural Strata]. Moscow, Nedra, 1984. 211 p. (In Russian)
2. Ilyin V.P. Chislennye metody resheniya zadach elektrofiziki [Numerical Methods for Solving Problems of Electrophysics]. Moscow, Nauka, 1985. 336 p. (In Russian)
3. Ladyzhenskaya O.A., Ural’tseva N.N. Lineinye i kvazilineinye uravneniya ellipticheskogo tipa [Linear and Quasilinear Equations of Elliptic Type]. Moscow, Nauka, 1973. 576 p. (In Russian)
4. Vladimirov V.S. Obobshchennye funktsii v matematicheskoi fizike [Generalized Functions in Mathematical Physics]. Moscow, Nauka, 1979. 320 p. (In Russian)
5. Vainberg M.M. Variatsionnye metody issledovaniya nelineinykh operatorov [Variational Methods for Studying Nonlinear Operators]. Moscow, Gostekhizdat, 1956. 344 p. (In Russian)
6. Lions J.-L. Nekotorye metody resheniya nelineinykh kraevykh zadach [Some Methods for Solving Nonlinear Boundary Value Problems]. Moscow, Mir, 1972. 587 p. (In Russian)
7. Gajewski H., Gr¨oger K., Zacharias K. Nelineinye operatornye uravneniya i operatornye differentsial’nye uravneniya [Nonlinear Operator Equations and Operator Differential Equations]. Moscow, Mir, 1978. 336 p. (In Russian)
8. Lyashko A.D., Karchevskii M.M. The solution of certain nonlinear problems of filtration theory. Sov. Math. (Izv. Vyssh. Uchebn. Zaved.), 1975, vol. 19, no. 6, pp. 60–66.
9. Zadvornov O.A. Investigation of a nonlinear stationary filtration problem in the presence of a point source. Russ. Math., 2005, vol. 49, no. 1, pp. 53–59.
10. Zadvornov O.A. Existence of solutions for quasilinear elliptic boundary value problem in the presence of point sources. Uchenye Zapiski Kazanskogo Universiteta. Seriya FizikoMatematicheskie Nauki, 2010, vol. 152, no. 1, pp. 155–163. (In Russian)
11. Zadvornov O.A., Zadvornova G.O. On the solution of a nonlinear stationary inhomogeneous filtration problem with a point source. Differ. Equations, 2014, vol. 50, no. 7, pp. 976–980. https://doi.org/10.1134/S0012266114070131.
12. Zadvornov O.A., Trifonova G.O. Iteration method for solving a nonlinear boundary value problem with a point source. Russ. Math., 2022, vol. 66, no. 5, pp. 60–64. https://doi.org/10.3103/S1066369X22050085.
Review
For citations:
Zadvornov O.А., Trifonova G.O. Mixed Boundary Value Problem for a Monotone Equation with a Lower Order Term and Point Sources on the Right Side. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(2):173-186. (In Russ.) https://doi.org/10.26907/2541-7746.2024.2.173-186
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