This article is cited in 7 papers

Initial-value problem for a higher-order partial quasilinear differential equation

T. K. Yuldashev^a, K. H. Shabadikov<sup>b

a</sup> M. F. Reshetnev Siberian State University of Science and Technologies
^b Ferghana State University

Abstract: 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.

UDC: 517.955.2

MSC: 35A30, 35C15, 35G55, 35L30

 English version: Journal of Mathematical Sciences (New York), 2021, 254:6, 811–822

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