Spectrum of a non-self-adjoint operator associated with the periodic heat equation

Details Spectrum of a non-self-adjoint operator associated with the periodic heat equation Spectrum of a non-self-adjoint operator associated with the periodic heat equation

2007-02-28

arxiv.org/abs/math-ph/0702100v1

Journal of Mathematical Analysis and its Applications, 342, 970-988, (2008)

Physics

Mathematical Physics

22 pages, 10 figures

Scientific paper

We study the spectrum of the linear operator $L = - \partial_{\theta} - \epsilon \partial_{\theta} (\sin \theta \partial_{\theta})$ subject to the periodic boundary conditions on $\theta \in [-\pi,\pi]$. We prove that the operator is closed in $L^2([-\pi,\pi])$ with the domain in $H^1_{\rm per}([-\pi,\pi])$ for $|\epsilon| < 2$, its spectrum consists of an infinite sequence of isolated eigenvalues and the set of corresponding eigenfunctions is complete. By using numerical approximations of eigenvalues and eigenfunctions, we show that all eigenvalues are simple, located on the imaginary axis and the angle between two subsequent eigenfunctions tends to zero for larger eigenvalues. As a result, the complete set of linearly independent eigenfunctions does not form a basis in $H^1_{\rm per}([-\pi,\pi])$.

Affiliated with

Also associated with

No associations

Rating

Spectrum of a non-self-adjoint operator associated with the periodic heat equation 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 Spectrum of a non-self-adjoint operator associated with the periodic heat equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectrum of a non-self-adjoint operator associated with the periodic heat equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-525082