Highly degenerate quasilinear parabolic systems
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....
Homogenization of periodic non self-adjoint problems with large drift and potential
We consider the homogenization of both the parabolic and eigenvalue problems for a singularly perturbed convection-diffusion equation in a periodic medium. All coefficients of the equation may vary both on the macroscopic scale and on the periodic microscopic scale. Denoting by ε the period, the potential or zero-order term is scaled as and the drift or first-order term is scaled as . Under a structural hypothesis on the first cell eigenvalue, which is assumed to admit a unique minimum in the...
Homotopy perturbation method for solving reaction-diffusion equations.
Hopf bifurcation with the spatial average of an activator in a radially symmetric free boundary problem.