Iterative methods for parabolic functional differential equations

Volume 40 / 2013

Milena Matusik Applicationes Mathematicae 40 (2013), 221-235 MSC: 35K20, 35K55, 35R10. DOI: 10.4064/am40-2-5

Abstract

This paper is concerned with iterative methods for parabolic functional differential equations with initial boundary conditions. Monotone iterative methods are discussed. We prove a theorem on the existence of solutions for a parabolic problem whose right-hand side admits a Jordan type decomposition with respect to the function variable. It is shown that there exist Newton sequences which converge to the solution of the initial problem. Differential equations with deviated variables and differential integral equations can be obtained from our general model by specializing given operators.

Authors

  • Milena MatusikInstitute of Mathematics
    University of Gdańsk
    Wit Stwosz Street 57
    80-952 Gdańsk, Poland
    e-mail

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