Mildly degenerate Kirchhoff equations with weak dissipation: Global existence and time decay |
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Authors: | Marina Ghisi |
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Affiliation: | a Università degli Studi di Pisa, Dipartimento di Matematica “Leonida Tonelli”, Pisa, Italy b Università degli Studi di Pisa, Dipartimento di Matematica Applicata “Ulisse Dini”, Pisa, Italy |
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Abstract: | 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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Keywords: | 35B25 35B40 35L70 35L80 |
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