A first-order partial differential equation of the common type with initial data in Cartesian coordinates on an infinite length line
S. N. Alekseenko1, L. E. Platonova2
| Annotation | The Cauchy problem for a quasi-linear first order partial differential equation is studied in case when initial data is given on an infinite length smooth line with non-vertical gradient. A system in 15 integral equations, a solution of which gives a solution of the considered Cauchy problem in original coordinates, is constructed. Local solvability conditions, which do not include in itself assumptions about behavior of the characteristic lines, are presented in a theorem announced here. |
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| Keywords | quasi-linear first order partial differential equation, Cauchy problem, method of an additional argument. |
1The professor of the applied mathematics chair, Nizhniy Novgorod State Technical University, Nizhniy Novgorod; sn-alekseenko@yandex.ru
2The assistant lecture of the mathematical analysis chair, Nizhniy Novgorod State Pedagogical University, Nizhniy Novgorod; fluff13@yandex.ru
Citation: S. N. Alekseenko, L. E. Platonova, "[A first-order partial differential equation of the common type with initial data in Cartesian coordinates on an infinite length line]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,14:3 (2012) 21–28 (In Russian)
