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

2009/03/16 by Marina Ghisi, Massimo Gobbino, Ghisi, Marina +1
Mathematics · #35B25 #35B40 #35L70 #35L80 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B25 #msc:35B40 #msc:35L70 #msc:35L80

paper · pdf · doi:10.48550/arxiv.0903.2713

25 pages

arxiv created 2009/03/16 · arxiv updated 2009/12/01

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 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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