Nonlocal  Solvability  of the Cauchy Problem for a System with  Negative Functions of the Variable $t$

Marina Dontsova

doi:10.52737/18291163-2023.15.4-1-10

Authors

Marina Dontsova Lobachevsky State University of Nizhny Novgorod

DOI:

https://doi.org/10.52737/18291163-2023.15.4-1-10

Keywords:

First-Order Partial Differential Equations, Cauchy Problem, Additional Argument Method, Global Estimates

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 $t$ 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 nonlocal solution of the Cauchy problem for a quasilinear system with negative functions of the variable $t$.

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