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arXiv · 0905.1358

Global Dissipativity and Inertial Manifolds for Diffusive Burgers Equations with Low-Wavenumber Instability

Jesenko Vukadinovic
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Abstract

Global well-posedness, existence of globally absorbing sets and existence of inertial manifolds is investigated for a class of diffusive Burgers equations. The class includes diffusive Burgers equation with nontrivial forcing, the Burgers-Sivashinsky equation and the Quasi-Stedy equation of cellular flames. The global dissipativity is proven in 2D for periodic boundary conditions. For the proof of the existence of inertial manifolds, the spectral-gap condition, which Burgers-type equations do not satisfy in its original form is circumvented by the Cole-Hopf transform. The procedure is valid in both one and two space dimensions.

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Jesenko Vukadinovic. 2009-05-09. Global Dissipativity and Inertial Manifolds for Diffusive Burgers Equations with Low-Wavenumber Instability. https://arxiv.org/abs/0905.1358

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