Global Attractors for the Generalized Wave Fronts in Chemical Reactions and Kuramoto-Sivashinsky Equations
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We consider a generalization of the evolution equation for wave fronts in chemical reactions. For this equation, we establish global well-posedness in weighted Sobolev spaces, Zs,1/2(R), s ≥ 1, and prove the existence of a global attractor in these spaces. In particular, our results also imply the existence of a global attractor for the Kuramoto-Sivashinsky (KS) equation in these spaces.