Hard implicit function theorem and small periodic solutions to partial differential equations
Homogenization of a carcinogenesis model with different scalings with the homogenization parameter
In the context of periodic homogenization based on two-scale convergence, we homogenize a linear system of four coupled reaction-diffusion equations, two of which are defined on a manifold. The system describes the most important subprocesses modeling the carcinogenesis of a human cell caused by Benzo-[a]-pyrene molecules. These molecules are activated to carcinogens in a series of chemical reactions at the surface of the endoplasmic reticulum, which constitutes a fine structure inside the cell....
Hopf bifurcation with the spatial average of an activator in a radially symmetric free boundary problem.
Hysteresis and Periodic Solutions of Semilinear and Quasilinear Wave Equations.