Mathematics – Analysis of PDEs
Scientific paper
2009-05-12
SIAM J. on Mathematical Analysis 43: 367-388 (2011)
Mathematics
Analysis of PDEs
22 pages, 2 pictures
Scientific paper
10.1137/090759495
We study the problem of finding the instability index of certain non-selfadjoint fourth order differential operators that appear as linearizations of coating and rimming flows, where a thin layer of fluid coats a horizontal rotating cylinder. The main result reduces the computation of the instability index to a finite-dimensional space of trigonometric polynomials. The proof uses Lyapunov's method to associate the differential operator with a quadratic form, whose maximal positive subspace has dimension equal to the instability index. The quadratic form is given by a solution of Lyapunov's equation, which here takes the form of a fourth order linear PDE in two variables. Elliptic estimates for the solution of this PDE play a key role. We include some numerical examples.
Burchard Almut
Chugunova Marina
No associations
LandOfFree
On computing the instability index of a non-selfadjoint differential operator associated with coating and rimming flows 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 On computing the instability index of a non-selfadjoint differential operator associated with coating and rimming flows, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On computing the instability index of a non-selfadjoint differential operator associated with coating and rimming flows will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337145