Geodesic
On continuous solutions to linear hyperbolic systems
Ma/lgorzata Zdanowicz1 ; Zbigniew Peradzy/nski2
1 Institute of Mathematics University of Bia/lystok Akademicka 2 15-267 Bia/lystok, Poland
2 Institute of Applied Mathematics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland and Institute of Fundamental Technological Research Polish Academy of Sciences Świ/etokrzyska 21 00-049 Warszawa, Poland
Annales Polonici Mathematici, Tome 86 (2005) no. 3, pp. 273-281 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the conditions under which the Cauchy problem for a linear hyperbolic system of partial differential equations of the first order in two independent variables has a unique continuous solution (not necessarily Lipschitz continuous). In addition to obvious continuity assumptions on coefficients and initial data, the sufficient conditions are the bounded variation of the left eigenvectors along the characteristic curves.
DOI : 10.4064/ap86-3-5
Keywords: study conditions under which cauchy problem linear hyperbolic system partial differential equations first order independent variables has unique continuous solution necessarily lipschitz continuous addition obvious continuity assumptions coefficients initial sufficient conditions bounded variation eigenvectors along characteristic curves

Ma/lgorzata Zdanowicz 1 ; Zbigniew Peradzy/nski 2

1 Institute of Mathematics University of Bia/lystok Akademicka 2 15-267 Bia/lystok, Poland
2 Institute of Applied Mathematics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland and Institute of Fundamental Technological Research Polish Academy of Sciences Świ/etokrzyska 21 00-049 Warszawa, Poland 
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Ma/lgorzata Zdanowicz; Zbigniew Peradzy/nski. On continuous solutions to linear hyperbolic systems. Annales Polonici Mathematici, Tome 86 (2005) no. 3, pp. 273-281. doi: 10.4064/ap86-3-5

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