Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates

Details Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates

2011-08-18

arxiv.org/abs/1108.3758v1

Mathematics

Analysis of PDEs

35 pages

Scientific paper

We consider degenerate Kirchhoff equations with a small parameter epsilon in front of the second-order time-derivative. It is well known that these equations admit global solutions when epsilon is small enough, and that these solutions decay as t -> +infinity with the same rate of solutions of the limit problem (of parabolic type). In this paper we prove decay-error estimates for the difference between a solution of the hyperbolic problem and the solution of the corresponding parabolic problem. These estimates show in the same time that the difference tends to zero both as epsilon -> 0, and as t -> +infinity. Concerning the decay rates, it turns out that the difference decays faster than the two terms separately (as t -> +infinity). Proofs involve a nonlinear step where we separate Fourier components with respect to the lowest frequency, followed by a linear step where we exploit weighted versions of classical energies.

Affiliated with

Also associated with

No associations

Rating

Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: decay-error estimates will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-181409