Global attractor for a modified Swift–Hohenberg equation
✍ Scribed by Mustafa Polat
- Book ID
- 108077307
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 382 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0898-1221
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📜 SIMILAR VOLUMES
We show using numerical simulations that a variety of localized patterns arise in a model equation: the quintic Swift-Hohenberg equation with complex coefficients. We demonstrate that various sizes of localized standing wave patterns are possible when the imaginary part of the complex coefficient is
differential equation with sectorial operator is shown to generate a dissipative semigroup whenever an appropriate introductory estimate for solutions is known. Based on Hale's theory of dissipative systems such an a priori estimate is then shown to be sufficient for existence of a global attractor.