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Efendiyev, M.A. ; Vougalter, V.*

Solvability of some Fredholm integro-differential equations with mixed diffusion in a square.

Discret. Contin. Dyn. Syst.-Ser. S, DOI: 10.3934/dcdss.2023124 (2023)
Verlagsversion DOI
We demonstrate the existence in the sense of sequences of solutions for some integro-differential type problems in a square in two dimensions with periodic boundary conditions. They contain the normal diffusion in one direction and the superdiffusion in the other direction. We work in a constrained subspace of H2 using the fixed point technique. The elliptic equation involves a second order differential operator satisfying the Fredholm property. It is established that, under reasonable technical assumptions, the convergence in the appropriate function spaces of the integral kernels yields the existence and convergence in H02 of the solutions. We generalize the results obtained in our preceding work [11] for the analogous equation considered in the whole R2 which contained a non-Fredholm operator.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Solvability conditions; Fredholm operators; Key phrases; tions; mixed diffusion; Properness Properties; Traveling-waves; Systems
ISSN (print) / ISBN 1937-1632
e-ISSN 1937-1179
Zeitschrift Discrete and Continuous Dynamical Systems - Series S
Verlag American Institute of Mathematical Sciences (AIMS)
Verlagsort Po Box 2604, Springfield, Mo 65801-2604, United States
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)