2021/02/27 by George Avalos, Avalos, George, Pelin G. Geredeli +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2103.00326
openalex publication_date 2021/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a multilayer hyperbolic-parabolic PDE system which constitutes a\ncoupling of 3D thermal - 2D elastic - 3D elastic dynamics, in which the\nboundary interface coupling between 3D fluid and 3D structure is realized via a\n2D elastic equation. Our main result here is one of strong decay for the given\nmultilayered - heat system. That is, the solution to this composite PDE system\nis stabilized asymptotically to the zero state.\n Our proof of strong stability takes place in the "frequency domain" and\nultimately appeals to the pointwise resolvent condition introduced by Tomilov\n[45]. This very useful result, however, requires that the semigroup associated\nwith our multilayered FSI system be completely non-unitary (c.n.u).\nAccordingly, we firstly establish that the semigroup e^ mathcal\nAt t\≥ 0 is indeed c.n.u., in part by invoking relatively recent\nresults of global uniqueness for overdetermined Lam 'e systems on nonsmooth\ndomains. Although the entire proof also requires higher regularity results for\nsome trace terms, this \"resolvent criterion approach" allows us to\nestablish a "classially soft" proof of strong decay. In particular, it avoids\nthe sort of technical PDE multipliers invoked in [9].\n