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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)
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
ISSN (print) / ISBN
2199-675X
e-ISSN
2199-6768
Journal
European Journal of Mathematics
Quellenangaben
Volume: 10,
Issue: 1
Publisher
Springer
Publishing Place
Gewerbestrasse 11, Cham, Ch-6330, Switzerland
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)
Grants
natural sciences and engineering research council of canada