Geodesic
Boundary value problems for composite type equations with a quasiparabolic operator in the leading part having the variable direction of evolution and discontinuous coefficients
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 2, pp. 7-17

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The solvability of boundary value problems for non-classical Sobolev type differential equations with an alternating function is studied. This function has a discontinuity of the first kind at the point zero and changes its sign depending on the sign of the variable $x$. The existence and uniqueness of regular solutions having generalized derivatives are proved. To this end we derived a priori estimates.
Mots-clés : Sobolev–type equation, variable direction of evolution, existence
Keywords: boundary value problem, differential operator, regular solution, uniqueness, a priory estimate. 
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     author = {A. I. Grigorieva and A. I. Kozhanov},
     title = {Boundary value problems for composite type equations with a quasiparabolic operator in the leading part having the variable direction of evolution and discontinuous coefficients},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {7--17},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_2_a0/}
}
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A. I. Grigorieva; A. I. Kozhanov. Boundary value problems for composite type equations with a quasiparabolic operator in the leading part having the variable direction of evolution and discontinuous coefficients. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 2, pp. 7-17. http://geodesic.mathdoc.fr/item/VSGU_2018_24_2_a0/