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Finite Dimensional Behavior for Forced Nonlinear Sobolev-Galpern Equations

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Abstract

This paper deals with the asymptotic behavior of solutions for the nonlinear Sobolev-Galpern equations. We first show the existence of the global weak attractor in \( H^{2} {\left( \Omega \right)} \cap H^{1}_{0} {\left( \Omega \right)} \) for the equations. And then by an energy equation we prove that the global weak attractor is actually the global strong attractor. The finite-dimensionality of the global attractor is also established.

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Authors and Affiliations

  1. Department of Mathematics, Guangzhou University, Guangzhou, 510405, China

    Ya-dong Shang

  2. Institute of Applied Physics and Computational Mathematics, 8009, Beijing, 100088, China

    Bo-ling Guo

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  1. Ya-dong Shang
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  2. Bo-ling Guo
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Correspondence to Ya-dong Shang.

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Supported by the National Natural Science Foundation of China (No. 10271034)

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Shang, Yd., Guo, Bl. Finite Dimensional Behavior for Forced Nonlinear Sobolev-Galpern Equations. Acta Mathematicae Applicatae Sinica, English Series 20, 247–256 (2004). https://doi.org/10.1007/s10255-004-0165-z

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  • DOI: https://doi.org/10.1007/s10255-004-0165-z

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