Existence and boundary regularity for degenerate phase transitions

Paolo Baroni; Tuomo Kuusi; Casimir Lindfors; José Miguel Urbano

doi:10.1137/17M1121585

Existence and boundary regularity for degenerate phase transitions

Paolo Baroni, Tuomo Kuusi, Casimir Lindfors, José Miguel Urbano

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

129 Lataukset (Pure)

Abstrakti

We study the Cauchy–Dirichlet problem associated to a phase transition modeled upon the degenerate two-phase Stefan problem. We prove that weak solutions are continuous up to the parabolic boundary and quantify the continuity by deriving a modulus. As a byproduct, these a priori regularity results are used to prove the existence of a so-called physical solution.

Alkuperäiskieli	Englanti
Sivut	456-490
Sivumäärä	35
Julkaisu	SIAM Journal on Mathematical Analysis
Vuosikerta	50
Numero	1
DOI - pysyväislinkit	https://doi.org/10.1137/17M1121585
Tila	Julkaistu - 1 tammikuuta 2018
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Pääsy asiakirjaan

10.1137/17M1121585

17m1121585Final published version, 507 KB

Link to publication in Scopus

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Siteeraa tätä

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AB - We study the Cauchy–Dirichlet problem associated to a phase transition modeled upon the degenerate two-phase Stefan problem. We prove that weak solutions are continuous up to the parabolic boundary and quantify the continuity by deriving a modulus. As a byproduct, these a priori regularity results are used to prove the existence of a so-called physical solution.

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KW - Degenerate equations

KW - Intrinsic scaling

KW - Stefan problem

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