This article is cited in 14 papers

Nonlocal solvability conditions for Cauchy problem for a system of first order partial differential equations with special right-hand sides

M. V. Dontsova

Nizhny Novgorod State Pedagogical University, Nizhny Novgorod, Russia

Abstract: We consider a Cauchy problem for a system of two quasilinear first order partial differential equations with special right-hand sides. We obtain the conditions of a nonlocal solvability of this Cauchy problem. The study of the nonlocal solvability of the Cauchy problem for a system of two quasilinear differential equations with special right-hand sides is based on the method of an additional argument. The proof of the nonlocal resolvability of the Cauchy problem for a system of two quasilinear first order partial differential equations with special right-hand sides relies on global estimates.

Keywords: first order partial differential equations, Cauchy problem, the method of an additional argument.

UDC: 517.9

MSC: 35F50, 35F55, 35A01, 35A02, 35A05

Received: 30.06.2014

 English version: Ufa Mathematical Journal, 2014, 6:4, 68–80

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