Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    An Inverse Parameter Problem With Generalized Impedance Boundary Condition for Two-Dimensional Linear Viscoelasticity
    (Society for Industrial and Applied Mathematics Publications, 2021) Ivanyshyn Yaman, Olha; Le Louer, Frederique; Le Louer, Frederique; Ivanyshyn Yaman, Olha; 04.02. Department of Mathematics; 01. Izmir Institute of Technology; 04. Faculty of Science
    We analyze an inverse boundary value problem in two-dimensional viscoelastic media with a generalized impedance boundary condition on the inclusion via boundary integral equation methods. The model problem is derived from a recent asymptotic analysis of a thin elastic coating as the thickness tends to zero [F. Caubet, D. Kateb, and F. Le Louer, J. Elasticity, 136 (2019), pp. 17-53]. The boundary condition involves a new second order surface symmetric operator with mixed regularity properties on tangential and normal components. The well-posedness of the direct problem is established for a wide range of constant viscoelastic parameters and impedance functions. Extending previous research in the Helmholtz case, the unique identification of the impedance parameters from measured data produced by the scattering of three independent incident plane waves is established. The theoretical results are illustrated by numerical experiments generated by an inverse algorithm that simultaneously recovers the impedance parameters and the density solution to the equivalent boundary integral equation reformulation of the direct problem.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 10
    Pseudo-Backstepping and Its Application To the Control of Korteweg-De Vries Equation From the Right Endpoint on a Finite Domain
    (Society for Industrial and Applied Mathematics Publications, 2019) Özsarı, Türker; Özsarı, Türker; Batal, Ahmet; Batal, Ahmet; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In this paper, we design Dirichlet-Neumann boundary feedback controllers for the Korteweg-de Vries equation that act at the right endpoint of the domain. The length of the domain is allowed to be critical. Constructing backstepping controllers that act at the right endpoint of the domain is more challenging than its left endpoint counterpart. The standard application of the backstepping method fails, because corresponding kernel models become overdetermined. In order to deal with this difficulty, we introduce the pseudo-backstepping method, which uses a pseudo-kernel that satisfies all but one desirable boundary condition. Moreover, various norms of the pseudo-kernel can be controlled through a parameter in one of its boundary conditions. We prove that the boundary controllers constructed via this pseudo-kernel still exponentially stabilize the system with the cost of a low exponential rate of decay. We show that a single Dirichlet controller is sufficient for exponential stabilization with a slower rate of decay. We also consider a second order feedback law acting at the right Dirichlet boundary condition. We show that this approach works if the main equation includes only the third order term, while the same problem remains open if the main equation involves the first order and/or the nonlinear terms. At the end of the paper, we give numerical simulations to illustrate the main result.