Monotone iteration for infinite systems of parabolic equations with functional dependence

Tom 90 / 2007

Anna Pudełko Annales Polonici Mathematici 90 (2007), 1-19 MSC: Primary 35K15; Secondary 35K55, 35R10, 35R45. DOI: 10.4064/ap90-1-1

Streszczenie

We consider the initial value problem for an infinite system of differential-functional equations of parabolic type. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. The solutions are obtained by the monotone iterative method. We prove theorems on weak partial differential-functional inequalities as well the existence and uniqueness theorems in the class of continuous bounded functions and in the class of functions satisfying a certain growth condition.

Autorzy

  • Anna PudełkoFaculty of Applied Mathematics
    AGH University of Science and Technology
    Al. Mickiewicza 30
    30-059 Kraków, Poland
    e-mail

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