Summary
We show that the weak solutions of the nonlinear hyperbolic system
converge, as ε tends to zero, to the solutions of the reduced problem
. Then they satisfy the nonlinear parabolic equation
. 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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Marcati, P., Milani, A.J. & Secchi, P. Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system. Manuscripta Math 60, 49–69 (1988). https://doi.org/10.1007/BF01168147
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DOI: https://doi.org/10.1007/BF01168147