Abstract:
We consider the Cauchy problem for a system of first-order quasilinear differential equations. The solvability of the problem is investigated in the initial coordinates using the additional argument method. Sufficient conditions for the existence and uniqueness of a local solution which has the same smoothness in the independent variable as the initial functions of the Cauchy problem are determined. An existence and uniqueness theorem of a local solution is proved. Sufficient conditions for the existence and uniqueness of a global solution are determined. The proof of the global solvability relies upon global estimates.
Key words:method of an additional argument, Cauchy problem, first-order partial differential equation.
Fulltext:
PDF file (257 kB)