Geodesic
Study of classical solution of a one-dimensional mixed problem for one class of fifth-order semilinear equations of the Korteweg–de Vries–Burgers type
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 436-455 
M. H. Sadykhov; K. I. Khudaverdiev. Study of classical solution of a one-dimensional mixed problem for one class of fifth-order semilinear equations of the Korteweg–de Vries–Burgers type. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 436-455. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

As is well known, many problems of mathematical physics are reduced to one- and multi-dimensional initial and initial–boundary value problems for, generally speaking, strongly nonlinear pseudoparabolic equations. The existence (local and global) and uniqueness of a classical solution to a one-dimensional mixed problem with homogeneous Riquier-type boundary conditions are analyzed for a class of fifth-order semilinear pseudoparabolic equations of the Korteweg–de Vries–Burgers type. For the classical solution of the mixed problem, a uniqueness theorem is proved using the Gronwall–Bellman inequality, a local existence theorem is proved by combining the generalized contraction mapping principle with the Schauder fixed point principle, and a global existence theorem is proved by applying the method of a priori estimates.

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