- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Advances in Numerical Analysis
Volume 2012 (2012), Article ID 731591, 24 pages
Signorini Cylindrical Waves and Shannon Wavelets
Department of Mathematics, University of Salerno, 84084 Fisciano (SA), Italy
Received 25 February 2012; Accepted 16 April 2012
Academic Editor: Doron Levy
Copyright © 2012 Carlo Cattani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- C. Cattani, “Waves in nonlinear Signorini structural model,” Journal of Mathematics, vol. 1, no. 2, pp. 97–106, 2008.
- C. Cattani and E. Nosova, “Transversal waves in nonlinear Signorini model,” Lecture Notes in Computer Science, vol. 5072, no. 1, pp. 1181–1190, 2008.
- C. Cattani and J. J. Rushchitsky, “Nonlinear plane waves in Signorini's hyperelastic material,” International Applied Mechanics, vol. 42, no. 8, pp. 895–903, 2006.
- C. Cattani and J. J. Rushchitsky, “Nonlinear cylindrical waves in Signorini's hyperelastic material,” International Applied Mechanics, vol. 42, no. 7, pp. 765–774, 2006.
- C. Cattani and J. J. Rushchitsky, “Similarities and differences between the Murnaghan and Signorini descriptions of the evolution of quadratically nonlinear hyperelastic plane waves,” International Applied Mechanics, vol. 42, no. 9, pp. 997–1010, 2006.
- C. Cattani, J. J. Rushchitsky, and J. Symchuk, “Nonlinear plane waves in hyperelastic medium deforming by Signorini law. Derivation of basic equations and identification of Signorini constant,” International Applied Mechanics, vol. 42, no. 10, pp. 58–67, 2006.
- A. Signorini, “Trasformazioni termoelastiche finite,” Annali di Matematica Pura ed Applicata, Series 4, vol. 22, no. 1, pp. 33–143, 1943.
- A. Signorini, “Trasformazioni termoelastiche finite,” Annali di Matematica Pura ed Applicata, Series 4, vol. 30, pp. 1–72, 1948.
- C. Cattani and J. J. Rushchitsky, Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure, vol. 74 of Series on Advances in Mathematics for Applied Sciences, World Scientific, Singapore, 2007.
- C. Cattani and J. J. Rushchitsky, “Volterra's distortions in nonlinear hyperelastic media,” International Journal of Applied Mathematics and Mechanics, vol. 1, no. 3, pp. 100–118, 2005.
- M. A. Biot, “Propagation of elastic waves in a cylindrical bore containing a fluid,” Journal of Applied Physics, vol. 23, no. 9, pp. 997–1005, 1952.
- H. Demiray, “Wave propagation through a viscous fluid contained in a prestressed thin elastic tube,” International Journal of Engineering Science, vol. 30, no. 11, pp. 1607–1620, 1992.
- H. H. Dai, “Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod,” Acta Mechanica, vol. 127, no. 1–4, pp. 193–207, 1998.
- C. Cattani, “Shannon wavelet in nonlinear cylindrical waves,” submitted to Ukrainian Mathematical Journal.
- G. Kaiser, A Friendly Guide to Wavelets, Birkhäuser, 2011.
- K. Amaratunga, J. R. Williams, S. Qian, and J. Weiss, “Wavelet-Galerkin solutions for one-dimensional partial differential equations,” International Journal for Numerical Methods in Engineering, vol. 37, no. 16, pp. 2703–2716, 1994.
- C. Cattani, “Harmonic wavelets towards the solution of nonlinear PDE,” Computers & Mathematics with Applications, vol. 50, no. 8-9, pp. 1191–1210, 2005.
- C. Cattani, “Connection coefficients of Shannon wavelets,” Mathematical Modelling and Analysis, vol. 11, no. 2, pp. 1–16, 2006.
- C. Cattani, “Shannon wavelets theory,” Mathematical Problems in Engineering, vol. 2008, Article ID 164808, 24 pages, 2008.
- C. Cattani, “Shannon wavelets for the solution of integrodifferential equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 408418, 22 pages, 2010.
- G. Beylkin and J. M. Keiser, “On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases,” Journal of Computational Physics, vol. 132, no. 2, pp. 233–259, 1997.
- S. Bertoluzza and G. Naldi, “A wavelet collocation method for the numerical solution of partial differential equations,” Applied and Computational Harmonic Analysis, vol. 3, no. 1, pp. 1–9, 1996.
- B. Alpert, G. Beylkin, R. Coifman, and V. Rokhlin, “Wavelet-like bases for the fast solution of second-kind integral equations,” SIAM Journal on Scientific Computing, vol. 14, pp. 159–184, 1993.
- W. Dahmen, S. Prössdorf, and R. Schneider, “Wavelet approximation methods for pseudodifferential equations: I Stability and convergence,” Mathematische Zeitschrift, vol. 215, no. 1, pp. 583–620, 1994.
- C. Cattani and Y. Y. Rushchitskii, “Solitary elastic waves and elastic wavelets,” International Applied Mechanics, vol. 39, no. 6, pp. 741–752, 2003.
- J. D. Achenbach, Wave Propagation in Elastic Solids, North-Holland, 1973.
- R. W. Ogden, Non-Linear Elastic Deformations, Dover, 1974.
- C. W. Macosko, Rheology: Principles, Measurement and Applications, VCH, 1994.
- A. Bower, Applied Mechanics of Solids, CRC, 2009.
- D. Zwillinger, Handbook of Differential Equations, Academic Press, Boston, Mass, USA, 3rd edition, 1997.
- I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, San Diego, Calif, USA, 6th edition, 2000.