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Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions

Sahbi Boussandel (2018)

Applications of Mathematics

The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet p -Laplace operator.

Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation

Martin Heida (2015)

Applications of Mathematics

We show existence of solutions to two types of generalized anisotropic Cahn-Hilliard problems: In the first case, we assume the mobility to be dependent on the concentration and its gradient, where the system is supplied with dynamic boundary conditions. In the second case, we deal with classical no-flux boundary conditions where the mobility depends on concentration u , gradient of concentration u and the chemical potential Δ u - s ' ( u ) . The existence is shown using a newly developed generalization of gradient...

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