Geometrical evolution of developed interfaces
Piero De Mottoni, M Schatzman · 2020
Consider the reaction-diffusion equation in ℝ N × ℝ + : u t – h 2 Δ u + φ ( u ) = 0 ; φ is the derivative of a bistable potential with wells of equal depth and h is a small parameter. If the initial data has an interface, we give an asymptotic expansion of arbitrarily high order and error estimates valid up to time O ( h −2 ). At lowest order, the interface evolves normally, with a velocity proportional to the mean curvature .