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Existence of solutions for some systems of integro-differential equations with transport and superdiffusion.
Anal. Math. Phys. 12:110 (2022)
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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Publication type
Article: Other
Keywords
Solvability Conditions ; Non Fredholm Operators ; Integro-differential Systems ; Drift Terms ; Superdiffusion
ISSN (print) / ISBN
1664-2368
e-ISSN
1664-235X
Quellenangaben
Volume: 12,
Issue: 5,
Article Number: 110
Publisher
Springer
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)
Grants
Robertson Chair grant