| Abstract: |
| We study the formation and evolution of complex morphologies that arise in systems of equations governed by nonlinear and nonlocal interactions. Starting from the continuum formulation, which is derived from a particular hydrodynamic limit of the lattice-based Blume-Capel model with Kawasaki dynamics, we analyze a class of partial differential equations that capture the interplay between diffusion and interaction-driven transport in a ternary mixture.
We propose a semi-discrete finite volume scheme to approximate the unique weak solution of the system. We prove that our scheme is well-posed and converge to the wanted solution. Furthermore, we show that the scheme is stable with respect to a parameter in the drift term. |
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