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

[摘要] 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.

[学科分类] 环境科学（综合）

[关键词] First-Order Partial Differential Equations;Cauchy Problem;Additional Argument Method;Global Estimates