The energy space and norm growth for abstract wave equations Original Research Article

For the wave equation View the MathML source (for tϵView the MathML source and ξϵView the MathML sourceNone could think that the natural associated energy space might be K := H1(View the MathML sourceN) × L2(View the MathML sourceN). 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 → ±∞).