On the local Cauchy problem for first order partial differential functional equations

Volume 98 / 2010

El/zbieta Pu/xniakowska-Ga/luch Annales Polonici Mathematici 98 (2010), 39-61 MSC: 35F25, 35R10. DOI: 10.4064/ap98-1-3


A theorem on the existence of weak solutions of the Cauchy problem for first order functional differential equations defined on the Haar pyramid is proved. The initial problem is transformed into a system of functional integral equations for the unknown function and for its partial derivatives with respect to spatial variables. The method of bicharacteristics and integral inequalities are applied. Differential equations with deviated variables and differential integral equations can be obtained from the general theory by specializing given operators.


  • El/zbieta Pu/xniakowska-Ga/luchInstitute of Mathematics
    University of Gda/nsk
    Wit Stwosz Street 57
    80-952 Gda/nsk, Poland

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