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

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

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.

DOI: 10.52737/18291163-2023.15.4-1-10 Armenian Journal of Mathematics, 15(4) 1-10

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Keywords

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

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