A numerical study of a degenerate diffusion equation driven by a Heaviside function
| Autor: | Raffaela Capitanelli, Carlo Alberini, S. Finzi Vita |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Heaviside step function
Mathematical analysis Degenerate energy levels Finite difference 010103 numerical & computational mathematics State (functional analysis) Function (mathematics) 01 natural sciences 010101 applied mathematics Computational Mathematics Nonlinear system symbols.namesake Computational Theory and Mathematics Modeling and Simulation free boundary problems Variational inequality symbols degenerate parabolic problems finite difference methods 0101 mathematics Diffusion (business) Mathematics |
| Popis: | 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 approach to the solution of this problem, using the exact Heaviside function or a regular approximation of it, showing the results of some numerical tests. |
| Databáze: | OpenAIRE |
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