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On the well‐posedness of a Volterra equation with applications in the Navier‐Stokes problem
Author(s) -
de Andrade Bruno
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4642
Subject(s) - mathematics , volterra equations , volterra integral equation , continuation , nonlinear system , viscoelasticity , mathematical analysis , interval (graph theory) , integral equation , computer science , physics , quantum mechanics , combinatorics , thermodynamics , programming language
This paper is dedicated to the study of a family of nonlinear Volterra equations coming from the theory of viscoelasticity. We analyze the existence of local mild solutions to the problem and their possible continuation to a maximal interval of existence. We also consider the problem of continuous dependence with respect to initial data.