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.

A numerical study of a degenerate diffusion equation driven by a Heaviside function / Alberini, C.; Capitanelli, R.; Finzi Vita, S.. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 89:(2021), pp. 139-149. [10.1016/j.camwa.2021.03.002]

A numerical study of a degenerate diffusion equation driven by a Heaviside function

Alberini, C.;Capitanelli, R.
;
Finzi Vita, S.
2021

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 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.
degenerate parabolic problems; finite difference methods; free boundary problems
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A numerical study of a degenerate diffusion equation driven by a Heaviside function / Alberini, C.; Capitanelli, R.; Finzi Vita, S.. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 89:(2021), pp. 139-149. [10.1016/j.camwa.2021.03.002]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1526964
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