How parabolic free boundaries approximate hyperbolic fronts

Brian H. Gilding; Roberto Natalini; Alberto Tesei

How parabolic free boundaries approximate hyperbolic fronts

Brian H. Gilding, Roberto Natalini, Alberto Tesei

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Abstract

Some recent results concerning existence and qualitative behaviour of the boundaries of the suppurts of solutions of the Cauchy problem for nonlinear first-order hyperbolic and second-order parabolic scalar conservation laws are discussed. Among other properties, it is shown that, under appropriate assumptions, parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit.

Original language	English
Pages (from-to)	62-67
Number of pages	6
Journal	Memoirs on differential equations and mathematical physics
Volume	12
Publication status	Published - 1997

Keywords

speed of propagation
shock waves
convection--diffusion equations
vanishing viscosity limit
EWI-16322
IR-70865
enthropy solutions
Conservation laws
METIS-140448

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Mem._Gilding_12_62
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Final published version, 2.92 MB

https://www.emis.de/journals/MDEMP/vol12/contents.htm

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title = "How parabolic free boundaries approximate hyperbolic fronts",

abstract = "Some recent results concerning existence and qualitative behaviour of the boundaries of the suppurts of solutions of the Cauchy problem for nonlinear first-order hyperbolic and second-order parabolic scalar conservation laws are discussed. Among other properties, it is shown that, under appropriate assumptions, parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit.",

keywords = "speed of propagation, shock waves, convection--diffusion equations, vanishing viscosity limit, EWI-16322, IR-70865, enthropy solutions, Conservation laws, METIS-140448",

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year = "1997",

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volume = "12",

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journal = "Memoirs on differential equations and mathematical physics",

issn = "1512-0015",

publisher = "Andrea Razmadze Mathematical Institute",

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T1 - How parabolic free boundaries approximate hyperbolic fronts

AU - Gilding, Brian H.

AU - Natalini, Roberto

AU - Tesei, Alberto

PY - 1997

Y1 - 1997

N2 - Some recent results concerning existence and qualitative behaviour of the boundaries of the suppurts of solutions of the Cauchy problem for nonlinear first-order hyperbolic and second-order parabolic scalar conservation laws are discussed. Among other properties, it is shown that, under appropriate assumptions, parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit.

AB - Some recent results concerning existence and qualitative behaviour of the boundaries of the suppurts of solutions of the Cauchy problem for nonlinear first-order hyperbolic and second-order parabolic scalar conservation laws are discussed. Among other properties, it is shown that, under appropriate assumptions, parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit.

KW - speed of propagation

KW - shock waves

KW - convection--diffusion equations

KW - vanishing viscosity limit

KW - EWI-16322

KW - IR-70865

KW - enthropy solutions

KW - Conservation laws

KW - METIS-140448

M3 - Article

VL - 12

SP - 62

EP - 67

JO - Memoirs on differential equations and mathematical physics

JF - Memoirs on differential equations and mathematical physics

SN - 1512-0015

ER -