Geodesic
Mixed problem for a higher-order nonlinear pseudoparabolic equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 73-83

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We examine the unique generalized solvability of the mixed problem for a higher-order nonlinear pseudoparabolic equation with two parameters in mixed derivatives. Using the Fourier variable separation method, we reduce the problem to a countable system of nonlinear integral equations whose unique solvability can be proved by the method of successive approximations. We prove the continuous dependence of a generalized solution to the mixed problem on the initial functions and the positive parameters.
Mots-clés : pseudoparabolic equation
Keywords: generalized derivative, method of successive approximations, parameter, unique solvability. 
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     author = {T. K. Yuldashev and K. H. Shabadikov},
     title = {Mixed problem for a higher-order nonlinear pseudoparabolic equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {73--83},
     publisher = {mathdoc},
     volume = {156},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_156_a5/}
}
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T. K. Yuldashev; K. H. Shabadikov. Mixed problem for a higher-order nonlinear pseudoparabolic equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 73-83. http://geodesic.mathdoc.fr/item/INTO_2018_156_a5/