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Exponential Attractor for a Nonlinear Boussinesq Equation

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Abstract

This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space \( H^{2}_{0} {\left( {0,1} \right)} \times L^{2} {\left( {0,1} \right)} \). The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space \( H^{3}_{0} {\left( {0,1} \right)} \times H^{1}_{0} {\left( {0,1} \right)} \).

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  1. Department of Mathematics, University of Jordan, Amman, 11942, Jordan

    Ahmed Y. Abdallah

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  1. Ahmed Y. Abdallah
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Correspondence to Ahmed Y. Abdallah.

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Abdallah, A.Y. Exponential Attractor for a Nonlinear Boussinesq Equation. Acta Math. Appl. Sin, Engl. Ser. 22, 443–450 (2006). https://doi.org/10.1007/s10255-006-0320-9

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  • DOI: https://doi.org/10.1007/s10255-006-0320-9

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