Initial-Value Problem for a Higher-Order Quasilinear Partial Differential Equation

We examine an initial-value problem for a certain higher-order quasilinear partial differential equation. Expressing the partial differential operator as the superposition of first-order operators, we apply methods of solution of first-order equations. We prove the unique solvability of the initial-...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 254; no. 6; pp. 811 - 822
Main Authors Yuldashev, T. K., Shabadikov, K. Kh
Format Journal Article
LanguageEnglish
Published New York Springer US 02.05.2021
Springer
Springer Nature B.V
Subjects
Differential equations
Linear equations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial differential equations
35L30
characteristics
35C15
35G55
initial-value problem
superposition of differential operators
directional derivative
35A30
unique solvability
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Summary:We examine an initial-value problem for a certain higher-order quasilinear partial differential equation. Expressing the partial differential operator as the superposition of first-order operators, we apply methods of solution of first-order equations. We prove the unique solvability of the initial-value problem considered.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05343-0