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Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space

We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn-Hilliard-Oono equation in the whole space R^3 with the non-linearity of the sub-quintic growth rate. Moreover, the dissipativity and the existence of a smooth global attractor in the naturally defined energy space is also verified. The result is crucially based on the Strichartz estimates for the linear Scroedinger equation in R^3.

preprint2014arXivOpen access
Anton SavostianovSergey Zelik
math.AP
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Anton SavostianovSergey Zelik

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