Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898614 | Journal of Differential Equations | 2018 | 32 Pages |
Abstract
We consider the wave equation with a boundary condition of memory type. Under natural conditions on the acoustic impedance of the boundary a corresponding semigroup of contractions is known to exist. With the help of quantified Tauberian theorems we establish energy decay rates via resolvent estimates on the generator of the semigroup. Using a variational approach, we reduce resolvent estimates to estimates for a sesquilinear form induced by an operator characteristic function arising form the matrix representation of the generator. Under not too strict additional assumptions on the acoustic impedance we establish an upper bound on the resolvent. For the wave equation on the interval or the disc we prove our estimates to be sharp.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Reinhard Stahn,