Geodesic
A boundary value problem for the third-order equation not solvable with respect to the highest-order derivative
Matematičeskie zametki SVFU, Tome 24 (2017), pp. 28-36

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We consider a boundary value problem for the third-order equation not solvable with respect to the highest-order derivative. Equations of this type, often called Sobolev type equations, occur in many applied problems. The nonstationary Galerkin method and regularization method are applied to prove the existence and uniqueness theorem for a regular solution of the boundary value problem. Also we obtain an error estimate via regularization parameter and in terms of eigenvalues of the spectral problem for the Laplace operator.
Mots-clés : pseudoparabolic equation
Keywords: boundary value problem, solvability, a priori estimate, approximate solution, error estimate. 
@article{SVFU_2017_24_a2,
     author = {I. E. Egorov and E. S. Efimova},
     title = {A boundary value problem for the third-order equation not solvable with respect to the highest-order derivative},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {28--36},
     publisher = {mathdoc},
     volume = {24},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2017_24_a2/}
}
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I. E. Egorov; E. S. Efimova. A boundary value problem for the third-order equation not solvable with respect to the highest-order derivative. Matematičeskie zametki SVFU, Tome 24 (2017), pp. 28-36. http://geodesic.mathdoc.fr/item/SVFU_2017_24_a2/