Boundary Stabilization of Parabolic Equations by Ionuţ Munteanu

Author:Ionuţ Munteanu
Language: eng
Format: epub, pdf
ISBN: 9783030110994
Publisher: Springer International Publishing

may have at most two distinct negative roots (since the free term is ). Denote them by . Assume that we have

i.e., is an eigenvalue of the Laplace operator of multiplicity , and is an eigenvalue of the Laplace operator of multiplicity . Of course, it may happen that only one of is an eigenvalue of the Laplace operator (we see that at least one is an eigenvalue in order not to have , which is in contradiction to the fact that is an eigenvector). In that case, all the discussion below can be easily revised, and one would arrive at similar conclusions. However, we will consider the “worst-case scenario,” namely that are both eigenvalues of the Lapalcian.

One can easily check that each vector from the systems

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