On continuous solutions to linear hyperbolic systems

Volume 86 / 2005

Ma/lgorzata Zdanowicz, Zbigniew Peradzy/nski Annales Polonici Mathematici 86 (2005), 273-281 MSC: Primary 35L45. DOI: 10.4064/ap86-3-5


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.


  • Ma/lgorzata ZdanowiczInstitute of Mathematics
    University of Bia/lystok
    Akademicka 2
    15-267 Bia/lystok, Poland
  • Zbigniew Peradzy/nskiInstitute of Applied Mathematics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    Institute of Fundamental Technological Research
    Polish Academy of Sciences
    Świ/etokrzyska 21
    00-049 Warszawa, Poland

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