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Pré-Publication, Document De Travail Année : 2020

Fourth order parabolic problem: a complex network approach

Résumé

In this paper we propose a novel approach for a fourth order differential problem using complex networks of reaction-diffusion equations. We model the biharmonic operator by a network, based on a finite graph, in which the coupling between nodes is linear. To this end, we study the fourth order parabolic 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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Dates et versions

hal-02478426 , version 1 (13-02-2020)

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  • HAL Id : hal-02478426 , version 1

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Guillaume Cantin, Alexandre Thorel. Fourth order parabolic problem: a complex network approach. 2020. ⟨hal-02478426⟩
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