Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay

Details Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay Mildly degenerate Kirchhoff equations with weak dissipation: global existence and time decay

2009-03-16

arxiv.org/abs/0903.2713v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

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 tends to +infinity. 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 tends to +infinity, with the same rate of the solution of the limit problem of parabolic type.

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