The energy space and norm growth for abstract wave equations
Applied Mathematics Letters, ISSN: 0893-9659, Vol: 16, Issue: 5, Page: 767-772
2003
- 13Citations
- 3Usage
- 2Captures
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Metrics Details
- Citations13
- Citation Indexes13
- 13
- CrossRef6
- Usage3
- Abstract Views3
- Captures2
- Readers2
Article Description
For the wave equation α2uαt2 = Σi=iN α2uαxi2 (for t ϵ R and ξ ϵ R N one 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 → ±∞).
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0893965903000806; http://dx.doi.org/10.1016/s0893-9659(03)00080-6; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84867968603&origin=inward; http://linkinghub.elsevier.com/retrieve/pii/S0893965903000806; http://api.elsevier.com/content/article/PII:S0893965903000806?httpAccept=text/xml; http://api.elsevier.com/content/article/PII:S0893965903000806?httpAccept=text/plain; https://linkinghub.elsevier.com/retrieve/pii/S0893965903000806; https://api.elsevier.com/content/article/PII:S0893965903000806?httpAccept=text/xml; https://api.elsevier.com/content/article/PII:S0893965903000806?httpAccept=text/plain; https://digitalcommons.memphis.edu/facpubs/5867; https://digitalcommons.memphis.edu/cgi/viewcontent.cgi?article=6866&context=facpubs; http://dx.doi.org/10.1016/s0893-9659%2803%2900080-6; https://dx.doi.org/10.1016/s0893-9659%2803%2900080-6
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