Infinite systems of first order PFDEs with mixed conditions

Volume 94 / 2008

W. Czernous Annales Polonici Mathematici 94 (2008), 209-230 MSC: 35R10, 35L60. DOI: 10.4064/ap94-3-2


We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems can be derived from the general model by specializing the operators.


  • W. CzernousInstitute of Mathematics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland

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