Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system

Pierangelo Marcati, Albert J. Milani, Paolo Secchi

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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
Issue number1
Publication statusPublished - Mar 1988


All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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