We study numerically the one-dimensional Allen–Cahn equation with spectral fractional Laplacian (−Δ)α/2 on intervals homogeneous Neumann boundary conditions. In particular, we are interested in speed of sharp interfaces approaching and annihilating each other. This process is known to be exponentially slow case classical Laplacian. Here investigate how width change if vary exponent α For associ...

Abstract: The paper concerns the existence of weak solutions to the Cahn-Hilliard-Gurtin system coupled with nonstationary elasticity. The system describes phase separation process in elastically stressed material. It generalizes the Cahn-Hilliard equation by admitting a more general structure and by coupling diffusive and elastic effects. The system is studied with the help of a singularly per...

We consider the problem of existence of entire solutions to the Allen-Cahn equation Δu + u - u(3) = 0 in , usually regarded as a prototype for the modeling of phase transition phenomena. In particular, exploiting the link between the Allen-Cahn equation and minimal surface theory in dimensions N ≥ 9, we find a solution, u, with ∂(x(N))u > 0, such that its level sets are close to a nonplanar, mi...