On the Bertozzi--Esedoglu--Gillette--Cahn--Hilliard Equation with Logarithmic Nonlinear Terms

Our aim in this paper is to study the existence of local (in time) solutions for the Bertozzi-Esedoglu-Gillette-Cahn-Hilliard equation with logarithmic nonlinear terms. This equation was proposed in view of applications to binary image inpainting. We also give some numerical simulations which show the efficiency of the model.