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Boundary stabilization of non-diagonal systems by proportional feedback forms

This work was supported by a grant of the Romanian Ministry of Research and Innovation, CNCS – UEFISCDI, project number PN-III-P1-1.1-TE-2019-0348, within PNCDI III
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  • In this work, we are concerned with the problem of boundary exponential stabilization, in a Hilbert space $ H $, of parabolic type equations, namely equations for which their linear parts generate analytic $ C_0- $semigroups. We consider the case where the projection of the linear leading operator, on a given Riesz basis of $ H $, is non-diagonal. We do not assume that the linear operator has compact resolvent. Therefore, the Riesz basis is not necessarily an eigenbasis. The boundary stabilizer is given in a simple linear feedback form, of finite-dimensional structure, involving only the Riesz basis. To illustrate the results, at the end of the paper, we provide an example of stabilization of a fourth-order evolution equation on the half-axis.

    Mathematics Subject Classification: Primary: 93D15.

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