Convergence of front propagation for anisotropic bistable reaction-diffusion equations

We study the convergence of the singularly perturbed anisotropic, nonhomogeneous reaction-diffusion equation epsilon partial derivative(t)u - epsilon(2) div T degrees(x,del u) + f(u) - epsilon(c(1)/c(0))g = 0, where f is the derivative of a bistable quartic-like potential with unequal wells, T degrees(x,) is a nonlinear monotone operator homogeneous of degree one and g is a given forcing term. More precisely, we prove that an appropriate level set of the solution satisfies an O(epsilon(3)\log epsilon\(2)) error bound (in the Hausdorff distance) with respect to a hypersurface moving with the geometric law V = (c - epsilon kappa(phi))n(phi) + g-dependent terms, where n(phi) is the so-called Cahn-Hoffmann vector and kappa(phi) denotes the anisotropic mean curvature of the hypersurface. We also discuss the connection between the anisotropic reaction-diffusion equation and the bidomain model, which is described by a system of equations modeling the propagation of an electric stimulus in the cardiac tissue.