Nonconvex mean curvature ow as a formal singular limit of the nonlinear bidomain model (Articolo in rivista)

Type
Label
  • Nonconvex mean curvature ow as a formal singular limit of the nonlinear bidomain model (Articolo in rivista) (literal)
Anno
  • 2013-01-01T00:00:00+01:00 (literal)
Alternative label
  • Bellettini, Giovanni; Paolini, Maurizio; Pasquarelli, Franco (2013)
    Nonconvex mean curvature ow as a formal singular limit of the nonlinear bidomain model
    in Advances in differential equations
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Bellettini, Giovanni; Paolini, Maurizio; Pasquarelli, Franco (literal)
Pagina inizio
  • 895 (literal)
Pagina fine
  • 934 (literal)
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  • http://projecteuclid.org/euclid.ade/1372777763 (literal)
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  • 18 (literal)
Rivista
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  • 40 (literal)
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  • 9-10 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientfica 1, 00133 Roma, Italy; INFN Laboratori Nazionali di Frascati (LNF), via E. Fermi 40, Frascati 00044 Roma, Italy. Dipartimento di Matematica, Università Cattolica \"Sacro Cuore\", via Trieste 17, 25121 Brescia, Italy; (literal)
Titolo
  • Nonconvex mean curvature ow as a formal singular limit of the nonlinear bidomain model (literal)
Abstract
  • In this paper we study the nonconvex anisotropic mean curvature flow of a hypersurface. This corresponds to an anisotropic mean curvature flow where the anisotropy has a nonconvex Prank diagram. The geometric evolution law is therefore forward-backward parabolic in character, hence ill-posed in general. We study a particular regularization of this geometric evolution, obtained with a nonlinear version of the so-called bidomain model. This is described by a degenerate system of two uniformly parabolic equations of reaction-diffusion type, scaled with a positive parameter e. We analyze some properties of the formal limit of solutions of this system as epsilon -> 0(+), and show its connection with nonconvex mean curvature flow. Several numerical experiments substantiating the formal asymptotic analysis are presented. (literal)
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