Publication Cover
Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 9
76
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Uniqueness results in the identification of distributed sources over Germain–Lagrange plates by boundary measurements

Pages 2004-2016 | Received 11 May 2014, Accepted 14 Aug 2015, Published online: 11 Sep 2015

References

  • Todhunter I. History of the theory of elasticity and of strength of materials, from Galilei to Lord Kelvin. Vol. I, New York (NY): Dover; 1960.
  • Kawano A. A uniqueness theorem for the determination of sources in the Germain--Lagrange plate equation. J. Math. Anal. Appl. 2013;402:191–200. Available from: http://linkinghub.elsevier.com/retrieve/pii/S0022247X13000395
  • Yamamoto M. Determination of forces in vibrations of beams and plates by pointwise and line observations. J. Inverse Ill-posed Prob. 1996;4:437–457.
  • Kawano A. Uniqueness in the determination of vibration sources in rectangular Germain--Lagrange plates using displacement measurements over line segments with arbitrary small length. Inverse Prob. 2013;29:085002. Available from: http://stacks.iop.org/0266-5611/29/i=8/a=085002?key=crossref.e628d0c2b901215a26441c2041bf2e1f
  • Alves C, Silvestre AL, Takahashi T, et al. Solving inverse source problems using observability. Applications to the Euler--Bernoulli plate equation. SIAM J. Control Optim. 2009;48:1632–1659. Available from: http://epubs.siam.org/doi/abs/10.1137/080725635
  • Zaïr O. Determination of point sources in vibrating plate by boundary measurements. Appl. Anal. 2013;92:2061–2075.
  • Yamamoto M, Zhang X. Global uniqueness and stability for an inverse wave source problem for less regular data. J. Math. Anal. Appl. 2001;263:479–500.
  • Nicaise S, Zair O. Identifiability, stability and reconstruction results of sources by interior measurements. Portugaliae Math. 2003;60:456–471.
  • Lions L. Contrôlabilité exacte, perturbations et stabilisation de systémes distribués [Exact controllability, stabilization and perturbations for distributed systems], tome 1, rma 8. Paris: Masson; 1988.
  • Folland GB. Introduction to partial differential equations. Princeton (NJ): Princeton University Press; 1995.
  • Treves F. Basic linear partial differential equations. New York (NY): Academic Press; 1975.
  • Mitrovic D, Zubrinic D. Fundamentals of applied functional analysis. Edinburgh Gate: Addison Wesley Longman; 1998.
  • Evans LC. Partial differential equations. Vol. 19, Providence (RI): American Mathematical Society; 1991.
  • Tucsnak M, Weiss G. Observation and control for operator semigroups. Basel: Birkhäuser; 2009. Available from: http://www.iecn.u-nancy.fr/tucsnak/obsbook.pdf
  • Kawano A, Zine A. Uniqueness and nonuniqueness results for a certain class of almost periodic distributions. SIAM J. Math. Anal. 2011;43:135–152.
  • Treves F. Topological vector spaces, distributions and kernels. Mineola (NY): Dover Publications; 2006.
  • Young RM. An introduction to nonharmonic Fourier series. Revised 1st ed. San Diego (CA): Academic Press; 2001.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.