A numerical study of an Heaviside function driven degenerate diffusion equation
Carlo Alberini,
Raffaela Capitanelli,
Stefano Finzi Vita
Abstract:We analyze a nonlinear degenerate parabolic problem whose diffusion coefficient is the Heaviside function of the distance of the solution itself from a given target function. We show that this model behaves as an evolutive variational inequality having the target as an obstacle: under suitable hypotheses, starting from an initial state above the target the solution evolves in time towards an asymptotic solution, eventually getting in contact with part of the target itself.We also study a finite difference appr… Show more
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