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

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Submitted: 2024-12-03; Published: 2024-12-03

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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.