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On a generalized diffusion problem: A complex network approach

Abstract : In this paper, we propose a new approach for studying a generalized diffusion problem, using complex networks of reaction-diffusion equations. We model the biharmonic operator by a network, based on a finite graph, in which the couplings between nodes are linear. To this end, we study the generalized diffusion problem, establishing results of existence, uniqueness and maximal regularity of the solution via operator sums theory and analytic semigroups techniques. We then solve the complex network problem and present sufficient conditions for the solutions of both problems to converge to each other. Finally, we analyze their asymptotic behavior by establishing the existence of a family of exponential attractors.
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https://hal.archives-ouvertes.fr/hal-03350365
Contributor : Guillaume CANTIN Connect in order to contact the contributor
Submitted on : Tuesday, September 21, 2021 - 11:40:00 AM
Last modification on : Thursday, May 19, 2022 - 3:27:17 PM

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Guillaume Cantin, Alexandre Thorel. On a generalized diffusion problem: A complex network approach. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2021, 27 (4), pp.2345-2365. ⟨10.3934/dcdsb.2021135⟩. ⟨hal-03350365⟩

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