Solvability of the Cauchy Problem for a Quasilinear System in Original Coordinates

We study the Cauchy problem for a system of quasilinear equations in the original coordinates by using the additional argument method. We obtain sufficient conditions for the existence and uniqueness of a local solution and show that the solution has the same x -smoothness as the initial function. W...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-10, Vol.249 (6), p.918-928
Main Author: Dontsova, M. V.
Format: Article
Language:English
Subjects:
Cauchy problems
Mathematics
Mathematics and Statistics
Smoothness
Uniqueness
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Summary:We study the Cauchy problem for a system of quasilinear equations in the original coordinates by using the additional argument method. We obtain sufficient conditions for the existence and uniqueness of a local solution and show that the solution has the same x -smoothness as the initial function. We also obtain sufficient conditions for the existence and uniqueness of a global solution. Bibliography: 4 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04984-x