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Title Cahn-Hilliard Equation with Nonlocal Singular Free Energies

Name Helmut Abels
Country Germany
Email helmut.abels@mathematik.uni-regensburg.de
Co-Author(s) Stefano Bosia, Maurizio Grasselli
Submit Time 2014-02-28 08:43:17
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
We consider the Cahn-Hilliard equation with a nonlocal free energy. In contrast to previous works the nonlocal part of the free energy is given by a strongly singular integral kernel, which gives rise to an integro-differential operator similar to a fractional power of the Laplacian. Moreover, the homogenuous free energy density is singular as well. We prove existence of a unique solution for all times and the existence of a global attractor. Finally, we discuss the boundary regularity of the solutions.