Geodesic
Riemann method for solving non-local boundary value problems for the third order pseudoparabolic equations
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 15-24.

Voir la notice de l'article provenant de la source Math-Net.Ru

The existence and uniqueness of regular solutions of non-local boundary value problems for the third order pseudoparabolic equations with variable coefficients are proved using the Riemann function method.
Keywords: boundary value problems, the Riemann function method, partial differential equation of the third order
Mots-clés : non-local condition, pseudoparabolic equation. 
@article{VSGTU_2013_4_a0,
     author = {M. H. Beshtokov},
     title = {Riemann method for solving non-local boundary value problems for the third order pseudoparabolic equations},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {15--24},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a0/}
}
TY  - JOUR
AU  - M. H. Beshtokov
TI  - Riemann method for solving non-local boundary value problems for the third order pseudoparabolic equations
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2013
SP  - 15
EP  - 24
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a0/
LA  - ru
ID  - VSGTU_2013_4_a0
ER  - 
%0 Journal Article
%A M. H. Beshtokov
%T Riemann method for solving non-local boundary value problems for the third order pseudoparabolic equations
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2013
%P 15-24
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a0/
%G ru
%F VSGTU_2013_4_a0
M. H. Beshtokov. Riemann method for solving non-local boundary value problems for the third order pseudoparabolic equations. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2013), pp. 15-24. http://geodesic.mathdoc.fr/item/VSGTU_2013_4_a0/

[1] G. I. Barenblatt, Yu. P. Zheltov, I. N. Kochina, “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]”, J. Appl. Math. Mech., 24:5 (1960), 1286–1303 | DOI | MR | Zbl

[2] E. S. Dzektser, “Equation of motion of underground water with a free surface in multilayer media”, Soviet Physics Doklady, 20:3 (1975), 24 | Zbl

[3] L. I. Rubinstein, “On the problem of the process of propagation of heat in heterogeneous media”, Izv. Akad. Nauk SSSR, Ser. Geogr., 12:1 (1948), 27–45

[4] T. W. Ting, “A cooling process according to two-temperature theory of heat conduction”, J. Math. Anal. Appl., 45:1 (1974), 23–31 | DOI | MR | Zbl

[5] M. Hallaire, S. de Parcevaux, R. J. Bouchet, et. al., L'eau et la production végétale, Institut National De La Recherche Agronomique, Paris, 1964, 455 pp.

[6] A. F. Chudnovsky, Thermophysics of the soil, Nauka, Moscow, 1976, 352 pp.

[7] D. Colton, “Pseudoparabolic equation in one space variable”, J. Diff. Eq., 12:3 (1972), 559–565 | DOI | MR | Zbl

[8] D. Colton, “Integral operators and the first initial-boundary value problems for pseudoparabolic equations with analytic coefficients”, J. Diff. Eq., 13:3 (1973), 506–522 | DOI | MR | Zbl

[9] M. Kh. Shkhanukov, “On some boundary-value problems for a third-order equation arising when modelling fluid filtration in porous media”, Differ. Uravn., 18:4 (1982), 689–699 | MR | Zbl

[10] A. F. Chudnovsky, “Some adjustments in the formulation and solution of problems of heat and moisture transfer in the soil”, Sb. Trudov AFI, 1969, no. 23, 41–54

[11] A. I. Kozhanov, “On a nonlocal boundary value problem with variable coefficients for the heat equation and the Aller equation”, Differ. Equ., 40:6 (2004), 815–826 | DOI | MR | Zbl