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Efendiyev, M.A. ; Vougalter, V.*

On solvability of some systems of Fredholm integro-differential equations with mixed diffusion in a square.

Eur. J. Math. 10, DOI: 10.1007/s40879-024-00729-1 (2024)
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We establish the existence in the sense of sequences of solutions for a certain system of integro-differential equations in a square in two dimensions with periodic boundary conditions involving the normal diffusion in one direction and the superdiffusion in the other direction in a constrained subspace of H2 for the vector functions via the fixed point technique. The system of elliptic equations contains a second order differential operator, which satisfies the Fredholm property. It is demonstrated that, under certain reasonable technical conditions, the convergence in the appropriate function spaces of the integral kernels implies the existence and convergence in Hc2(Ω,RN) of the solutions. We generalize our results derived in Efendiev and Vougalter (J Dyn Differ Equ, 2022. https://doi.org/10.1007/s10884-022-10199-2) for an analogous system studied in the whole R2 which involved non-Fredholm operators. Let us emphasize that the study of systems is more complicated than the scalar case.
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Publication type Article: Journal article
Document type Scientific Article
Keywords 35p30 ; 47f05 ; 47g20 ; Fredholm Operators ; Integro-differential Systems ; Mixed Diffusion ; Solvability Conditions; Properness Properties; Stationary Solutions; Traveling-waves; Existence
Language english
Publication Year 2024
HGF-reported in Year 2024
ISSN (print) / ISBN 2199-675X
e-ISSN 2199-6768
Journal European Journal of Mathematics
Quellenangaben Volume: 10, Issue: 1 Pages: , Article Number: , Supplement: ,
Publisher Springer
Publishing Place Gewerbestrasse 11, Cham, Ch-6330, Switzerland
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)
POF-Topic(s) 30205 - Bioengineering and Digital Health
Research field(s) Enabling and Novel Technologies
PSP Element(s) G-503800-001
Grants natural sciences and engineering research council of canada
DOI 10.1007/s40879-024-00729-1
WOS ID 001173712500001
Scopus ID 85186887235
Erfassungsdatum 2024-05-08
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