Solvability of mixed problems for heat equations with two nonlocal conditions
-
Onur Alp İlhan
,
Danyal Soybaş
Abstract
In this study, the solvability of a problem of the heat conduction theory with two nonlocal boundary conditions is investigated. Systems of eigenfunctions of the corresponding operator with two nonlocal boundary conditions are taken into consideration. A theorem on the solvability of the problem of the theory of heat conduction with two nonlocal boundary conditions is given
( Communicated by Alberto Lastra )
References
[1] Bary, N. K: Biorthogonal systems and bases in Hilbert space, Uch. Zap. MGU, Matematika 148(4) (1951), 69–107.Suche in Google Scholar
[2] Cannon, J. R.: The solution of heat equation subject to the specification of energy, Quart. Appl. Math. 21(2) (1963), 155–160.10.1090/qam/160437Suche in Google Scholar
[3] İlhan, O. A.–-Kasimov, Sh. G.–-Rakhmanov, F. D.–-Baskonus, H. M.: On the solvability of a problem of the heat conduction theory with two nonlocal conditions. Abstract Book of the 4th International Conference on Computational Mathematics and Engineering Sciences, April, 2019Suche in Google Scholar
[4] Il’in, V. A.: On the solvability of mixed problems for hyperbolic and parabolic equations, Uspekhi Mat. Nauk. 15(2) (1960), 97–154.10.1070/RM1960v015n02ABEH004217Suche in Google Scholar
[5] Il’in, V. A.: Necessary and sufficient conditions for a subsystem of the eigen- and associated functions of a Keldys bundle of ordinary differential operators to be a basis, Dokl. Akad. Nauk SSSR 227 (1976), 796–799, Engl. transl.: Soviet Math. Dokl. 17 (1976), 513–516.Suche in Google Scholar
[6] Ionkin, N. I.: The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition, Differ. Uravn. 13(2) (1977), 294–304.Suche in Google Scholar
[7] Kasimov, S. G.–-Rakhmanov, F. D.: On a spectral problem of the heat conduction theory with nonlocal boundary conditions, Tashkent Vestnik NUUz 2 (2013), 83–86.Suche in Google Scholar
[8] Kasimov, S. .G.–-Rakhmanov, F. D.: On a spectral problem of the heat conduction theory with nonlocal boundary conditions of the Samarskii-Ionkin type, Tashkent Vestnik NUUz 1–2 (2014).Suche in Google Scholar
[9] Naimark, M. A.: Linear Differential Operators, Nauka, Moscow, 1969.Suche in Google Scholar
[10] Tikhonov, A. N.–-Samarskii, A. A.: Equations of Mathematical Physics, Nauka, Moscow, 1977.Suche in Google Scholar
© 2022 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Prof. RNDr. Július korbaš, CSC. passed away
- Kalmbach measurability In d0-algebras
- Quantifiers on L-algebras
- Ideals of functions with compact support in the integer-valued case
- An algebraic study of the logic S5’(BL)
- Triangular numbers and generalized fibonacci polynomial
- A general matrix series inversion pair and associated polynomials
- Quantum ostrowski type inequalities for pre-invex functions
- Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
- Approximating families for lattice outer measures on unsharp quantum logics
- On a generalized Lamé-Navier system in ℝ3
- Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
- On some classical properties of normed spaces via generalized vector valued almost convergence
- Fan-Hemicontinuity for the gradient of the norm in Hilbert space
- Solvability of mixed problems for heat equations with two nonlocal conditions
- The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
- A note on set-star-K-Menger spaces
- A bivariate extension of the Omega distribution for two-dimensional proportional data
- Bernstein polynomials based iterative method for solving fractional integral equations
- The symmetric 4-Player gambler’s problem with unequal initial stakes
- Enveloping action: Convergence spaces
Artikel in diesem Heft
- Prof. RNDr. Július korbaš, CSC. passed away
- Kalmbach measurability In d0-algebras
- Quantifiers on L-algebras
- Ideals of functions with compact support in the integer-valued case
- An algebraic study of the logic S5’(BL)
- Triangular numbers and generalized fibonacci polynomial
- A general matrix series inversion pair and associated polynomials
- Quantum ostrowski type inequalities for pre-invex functions
- Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
- Approximating families for lattice outer measures on unsharp quantum logics
- On a generalized Lamé-Navier system in ℝ3
- Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
- On some classical properties of normed spaces via generalized vector valued almost convergence
- Fan-Hemicontinuity for the gradient of the norm in Hilbert space
- Solvability of mixed problems for heat equations with two nonlocal conditions
- The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
- A note on set-star-K-Menger spaces
- A bivariate extension of the Omega distribution for two-dimensional proportional data
- Bernstein polynomials based iterative method for solving fractional integral equations
- The symmetric 4-Player gambler’s problem with unequal initial stakes
- Enveloping action: Convergence spaces
