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Efendiyev, M.A. ; Vougalter, V.*

Existence of solutions for some systems of integro-differential equations with transport and superdiffusion.

Anal. Math. Phys. 12:110 (2022)
DOI
We establish the existence in the sense of sequences of solutions for certain systems of integro-differential equations which involve the drift terms and the square root of the one dimensional negative Laplace operator, on the whole real line or on a finite interval with periodic boundary conditions in the corresponding H2 spaces. The argument is based on the fixed point technique when the elliptic systems contain first order differential operators with and without Fredholm property. It is proven that, under the reasonable technical conditions, the convergence in L1 of the integral kernels yields the existence and convergence in H2 of the solutions. We emphasize that the study of the systems is more complicated than of the scalar case and requires to overcome more cumbersome technicalities.
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Publikationstyp Artikel: Sonstiges
Korrespondenzautor
Schlagwörter Solvability Conditions ; Non Fredholm Operators ; Integro-differential Systems ; Drift Terms ; Superdiffusion
ISSN (print) / ISBN 1664-2368
e-ISSN 1664-235X
Zeitschrift Analysis and Mathematical Physics
Quellenangaben Band: 12, Heft: 5, Seiten: , Artikelnummer: 110 Supplement: ,
Verlag Springer
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)
Förderungen Robertson Chair grant