Hyperbolic–parabolic singular perturbation for nondegenerate Kirchhoff equations with critical weak dissipation
نویسندگان
چکیده
We consider the hyperbolic-parabolic singular perturbation problem for a nondegenerate quasilinear equation of Kirchhoff type with weak dissipation. This means that the dissipative term is multiplied by a coefficient b(t) which tends to 0 as t→ +∞. The case where b(t) ∼ (1 + t) with p < 1 has recently been considered. The result is that the hyperbolic problem has a unique global solution, and the difference between solutions of the hyperbolic problem and the corresponding solutions of the parabolic problem converges to zero both as t→ +∞ and as ε→ 0. In this paper we show that these results cannot be true for p > 1, but they remain true in the critical case p = 1. Mathematics Subject Classification 2000 (MSC2000): 35B25, 35B40, 35L70.
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