Ghisi, Marina and Gobbino, Massimo (2010) Mildly degenerate Kirchhoff equations with weak dissipation: Global existence and time decay. Journal of Differential Equations, 248/20 (2). pp. 381-402. ISSN 0022-0396
SUMMARY We consider the hyperbolic-parabolic singular perturbation problem for a degenerate quasilinear Kirchhoff equation with weak dissipation. This means that the coefficient of the dissipative term tends to zero when t → +∞. We prove that the hyperbolic problem has a unique global solution for suitable values of the parameters. We also prove that the solution decays to zero, as t → +∞, with the same rate of the solution of the limit problem of parabolic type.
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