Infinite‐energy solutions for the Cahn–Hilliard equation in cylindrical domains. (5th August 2013)

• Record Type: Journal Article
• Authors: Eden, A.; Kalantarov, V.K.; Zelik, S.V.
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 13(2014:Sep. 15)
• Page Start: 1884
• Page End: 1908
• Publication Date: 2013-08-05
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2942
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2942-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2942-para-0001">We give a detailed study of the infinite‐energy solutions of the Cahn–Hilliard equation in the 3D cylindrical domains in uniformly local phase space. In particular, we establish the well‐posedness and dissipativity for the case of regular potentials of arbitrary polynomial growth as well as for the case of sufficiently strong singular potentials. For these cases, we prove the further regularity of solutions and the existence of a global attractor. For the cases where we have failed to prove the uniqueness (e.g., for the logarithmic potentials), we establish the existence of the trajectory attractor and study its properties. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>