Convergence of hydrodynamical limits for generalized carleman models

Hironari Miyoshi; Masayoshi Tsutsumi

doi:10.1619/fesi.59.351

Convergence of hydrodynamical limits for generalized carleman models

Hironari Miyoshi, Masayoshi Tsutsumi

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider the initial-boundary value problem for a 2-speed system of first order semilinear hyperbolic equations. We establish the existence of global weak solutions in L¹ by the theory of nonlinear contraction semigroups. Using the monotone method and the div-curl lemma, we investigate the hydrodynamical limits of the solutions of the hyperbolic systems and show that the limits verify the doubly nonlinear parabolic equations.

Original language	English
Pages (from-to)	351-382
Number of pages	32
Journal	Funkcialaj Ekvacioj
Volume	59
Issue number	3
DOIs	https://doi.org/10.1619/fesi.59.351
Publication status	Published - 2016

Keywords

Carleman’s equation
Div-curl lemma
Hydrodynamical limit
Monotone method

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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abstract = "We consider the initial-boundary value problem for a 2-speed system of first order semilinear hyperbolic equations. We establish the existence of global weak solutions in L1 by the theory of nonlinear contraction semigroups. Using the monotone method and the div-curl lemma, we investigate the hydrodynamical limits of the solutions of the hyperbolic systems and show that the limits verify the doubly nonlinear parabolic equations.",

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author = "Hironari Miyoshi and Masayoshi Tsutsumi",

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AU - Tsutsumi, Masayoshi

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AB - We consider the initial-boundary value problem for a 2-speed system of first order semilinear hyperbolic equations. We establish the existence of global weak solutions in L1 by the theory of nonlinear contraction semigroups. Using the monotone method and the div-curl lemma, we investigate the hydrodynamical limits of the solutions of the hyperbolic systems and show that the limits verify the doubly nonlinear parabolic equations.

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KW - Div-curl lemma

KW - Hydrodynamical limit

KW - Monotone method

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Convergence of hydrodynamical limits for generalized carleman models

Abstract

Keywords

ASJC Scopus subject areas

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