LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

On the decay rate for the wave equation with viscoelastic boundary damping

Photo from archive.org

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… Click to show full abstract

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: viscoelastic boundary; equation viscoelastic; decay rate; rate wave; equation; wave equation

Journal Title: Journal of Differential Equations
Year Published: 2017

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.