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Volume 39, Issue 4
Approximation of the Long-Time Dynamics of the Dynamical System Generated by the Ginzburg-Landau Equation

Cristina Tone & Florentina Tone

DOI: 10.4208/cmr.2023-0003

Commun. Math. Res., 39 (2023), pp. 501-522.

Published online: 2023-11

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  • Abstract

In this article we consider the (complex) Ginzburg-Landau equation, we discretize in time using the implicit Euler scheme, and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

  • Keywords

Ginzburg-Landau equation, implicit Euler scheme, long-time stability, attractors.

  • AMS Subject Headings

35Q56, 35Q35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-39-501, author = {Tone , Cristina and Tone , Florentina}, title = {Approximation of the Long-Time Dynamics of the Dynamical System Generated by the Ginzburg-Landau Equation}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {39}, number = {4}, pages = {501--522}, abstract = {

In this article we consider the (complex) Ginzburg-Landau equation, we discretize in time using the implicit Euler scheme, and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0003}, url = {http://global-sci.org/intro/article_detail/cmr/22098.html} }
TY - JOUR T1 - Approximation of the Long-Time Dynamics of the Dynamical System Generated by the Ginzburg-Landau Equation AU - Tone , Cristina AU - Tone , Florentina JO - Communications in Mathematical Research VL - 4 SP - 501 EP - 522 PY - 2023 DA - 2023/11 SN - 39 DO - http://doi.org/10.4208/cmr.2023-0003 UR - https://global-sci.org/intro/article_detail/cmr/22098.html KW - Ginzburg-Landau equation, implicit Euler scheme, long-time stability, attractors. AB -

In this article we consider the (complex) Ginzburg-Landau equation, we discretize in time using the implicit Euler scheme, and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

Tone , Cristina and Tone , Florentina. (2023). Approximation of the Long-Time Dynamics of the Dynamical System Generated by the Ginzburg-Landau Equation. Communications in Mathematical Research . 39 (4). 501-522. doi:10.4208/cmr.2023-0003
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