Armenian Journal of Mathematics, 15(4)
2023; 1–10
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Nonlocal Solvability of the Cauchy Problem for a System with Negative Functions of the Variable t

Marina Dontsova*

Received: 2024-12-04 · Published: 2023-03-22

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CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Nonlocal Solvability of the Cauchy Problem for a System with Negative Functions of the Variable t
Author
Marina Dontsova
Source journal
Armenian Journal of Mathematics, 15(4)
Published
2023-03-22
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2023.15.4-1-10

Abstract

We obtain sufficient conditions for the existence and uniqueness of a local solution of the Cauchy problem for a quasilinear system with negative functions of the variable tt and show that the solution has the same xx-smoothness as the initial function. We also obtain sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem for a quasilinear system with negative functions of the variable tt.
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