Geodesic
Initial-value problem for a higher-order partial quasilinear differential equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 106-116

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We examine an initial-value problem for a certain higher-order partial quasilinear differential equation. Expressing the partial differential operator as the superposition of first-order operator, we apply methods of solution of first-order equations. We prove the unique solvability of the initial-value problem considered.
Keywords: initial-value problem, characteristics, directional derivative, superposition of differential operators, unique solvability. 
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     author = {T. K. Yuldashev and K. H. Shabadikov},
     title = {Initial-value problem for a higher-order partial quasilinear differential equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {106--116},
     publisher = {mathdoc},
     volume = {156},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_156_a9/}
}
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T. K. Yuldashev; K. H. Shabadikov. Initial-value problem for a higher-order partial quasilinear differential equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 106-116. http://geodesic.mathdoc.fr/item/INTO_2018_156_a9/