### 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 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Marcati, P., Milani, A. J., & Secchi, P. (1988). Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system.

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