"The energy space and norm growth for abstract wave equations" by J. A. Goldstein and M. Wacker
 

The energy space and norm growth for abstract wave equations

Abstract

For the wave equation α2u αt2 = Σ i=i N α2u αx(i)α2 (for t ε R and ξ ε R None could think that the natural associated energy space might be K:= H 1(R N) × L 2(R N). This is misleading and only partially correct. The purpose of this paper is to explain the role of the energy spaces associated with a wave equation. This is done in an abstract context, when the negative Laplacian is replaced by an arbitrary nonnegative self-adjoint operator on a Hilbert space. For the wave equation on κ, the norm of the governing group of operators is shown to grow linearly in time (as t → ±∞). © 2003 Elsevier Science Ltd. All rights reserved.

Publication Title

Applied Mathematics Letters

Plum Print visual indicator of research metrics
PlumX Metrics
  • Citations
    • Citation Indexes: 13
  • Usage
    • Abstract Views: 3
  • Captures
    • Readers: 2
see details

Share

COinS