### 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 language | English |
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Pages (from-to) | 49-69 |

Number of pages | 21 |

Journal | Manuscripta Mathematica |

Volume | 60 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1988 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Manuscripta Mathematica*,

*60*(1), 49-69. https://doi.org/10.1007/BF01168147

}

*Manuscripta Mathematica*, vol. 60, no. 1, pp. 49-69. https://doi.org/10.1007/BF01168147

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system

AU - Marcati, Pierangelo

AU - Milani, Albert J.

AU - Secchi, Paolo

PY - 1988/3

Y1 - 1988/3

N2 - 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).

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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UR - http://www.scopus.com/inward/citedby.url?scp=0002662053&partnerID=8YFLogxK

U2 - 10.1007/BF01168147

DO - 10.1007/BF01168147

M3 - Article

AN - SCOPUS:0002662053

VL - 60

SP - 49

EP - 69

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1

ER -