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

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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 - Milani, Albert J.

AU - Secchi, Paolo

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