Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system

Pierangelo Marcati, Albert J. Milani, Paolo Secchi

    Research output: Contribution to journalArticle

    33 Citations (Scopus)

    Abstract

    We show that the weak solutions of the nonlinear hyperbolic system {Mathematical expression} converge, as ε tends to zero, to the solutions of the reduced problem {Mathematical expression}. Then they satisfy the nonlinear parabolic equation {Mathematical expression}. The limiting procedure is carried out using the techniques of "Compensated Compactness". Some connections with the theory of nonlinear heat conduction and the theory of nonlinear diffusion in a porous medium are suggested. The main result is stated in th. (2.9).

    Original languageEnglish
    Pages (from-to)49-69
    Number of pages21
    JournalManuscripta Mathematica
    Volume60
    Issue number1
    DOIs
    Publication statusPublished - Mar 1988

    Fingerprint

    Hyperbolic Systems
    Weak Solution
    Nonlinear Hyperbolic Systems
    Compensated Compactness
    Nonlinear Parabolic Equations
    Nonlinear Diffusion
    Heat Conduction
    Porous Media
    Limiting
    Tend
    Converge
    Zero

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)

    Cite this

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    Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system. / Marcati, Pierangelo; Milani, Albert J.; Secchi, Paolo.

    In: Manuscripta Mathematica, Vol. 60, No. 1, 03.1988, p. 49-69.

    Research output: Contribution to journalArticle

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    AU - Marcati, Pierangelo

    AU - Milani, Albert J.

    AU - Secchi, Paolo

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    AB - We show that the weak solutions of the nonlinear hyperbolic system {Mathematical expression} converge, as ε tends to zero, to the solutions of the reduced problem {Mathematical expression}. Then they satisfy the nonlinear parabolic equation {Mathematical expression}. The limiting procedure is carried out using the techniques of "Compensated Compactness". Some connections with the theory of nonlinear heat conduction and the theory of nonlinear diffusion in a porous medium are suggested. The main result is stated in th. (2.9).

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