The nonlinear multidomain model: a new formal asymptotic analysis

Maurizio Paolini; Giovanni Bellettini; Stefano Amato

The nonlinear multidomain model: a new formal asymptotic analysis

Maurizio Paolini
, Giovanni Bellettini
, Stefano Amato

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

Original language	English
Title of host publication	Geometric Partial Differential Equations proceedings
Publisher	Scuola Normale Superiore di Pisa
Pages	33-74
Number of pages	42
ISBN (Print)	88-7642-472-4
Publication status	Published - 2013

Keywords

anisotropy
asymptotic analysis
illposed problems
mean curvature flow

Cite this

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title = "The nonlinear multidomain model: a new formal asymptotic analysis",

abstract = "We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.",

keywords = "anisotropy, asymptotic analysis, illposed problems, mean curvature flow, anisotropy, asymptotic analysis, illposed problems, mean curvature flow",

author = "Maurizio Paolini and Giovanni Bellettini and Stefano Amato",

year = "2013",

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TY - CHAP

T1 - The nonlinear multidomain model: a new formal asymptotic analysis

AU - Paolini, Maurizio

AU - Bellettini, Giovanni

AU - Amato, Stefano

PY - 2013

Y1 - 2013

N2 - We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

AB - We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be the dual of the star-shaped combination of the m original anisotropies.

KW - anisotropy

KW - asymptotic analysis

KW - illposed problems

KW - mean curvature flow

KW - anisotropy

KW - asymptotic analysis

KW - illposed problems

KW - mean curvature flow

UR - https://publicatt.unicatt.it/handle/10807/52287

M3 - Chapter

SN - 88-7642-472-4

SP - 33

EP - 74

BT - Geometric Partial Differential Equations proceedings

PB - Scuola Normale Superiore di Pisa

ER -

The nonlinear multidomain model: a new formal asymptotic analysis

Abstract

Keywords

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