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Chevron Pattern Equations: Exponential Attractor and Global Stabilization

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Abstract

The initial boundary value problem for a nonlinear system of equations modeling the chevron patterns is studied in one and two spatial dimensions. The existence of an exponential attractor and the stabilization of the zero steady state solution through application of a finite-dimensional feedback control is proved in two spatial dimensions. The stabilization of an arbitrary fixed solution is shown in one spatial dimension along with relevant numerical results.

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Technion-Israel Institute of Technology, 3200003, Haifa, Israel

    Habiba Kalantarova

  2. Department of Mathematics, Koç University, Istanbul, Turkey

    Varga Kalantarov

  3. Azerbaijan State Oil and Industry University, Baku, Azerbaijan

    Varga Kalantarov

  4. Lightricks Ltd., Jerusalem, Israel

    Orestis Vantzos

Authors
  1. Habiba Kalantarova
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  2. Varga Kalantarov
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  3. Orestis Vantzos
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Correspondence to Varga Kalantarov.

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Dedicated to Enrique Zuazua on the occasion of his 60th birthday.

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Kalantarova, H., Kalantarov, V. & Vantzos, O. Chevron Pattern Equations: Exponential Attractor and Global Stabilization. Vietnam J. Math. 49, 901–918 (2021). https://doi.org/10.1007/s10013-021-00486-8

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  • DOI: https://doi.org/10.1007/s10013-021-00486-8

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