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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 546083, 9 pages
Weak Equivalence Transformations for a Class of Models in Biomathematics
1Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), Rua Santa Adélia 166, Bairro Bangu, 09.210-170 Santo André, SP, Brazil
2Dipartimento di Matematica e Informatica, Università Degli Studi di Catania, Viale Andrea Doria 6, 95125 Catania, Italy
Received 29 November 2013; Accepted 11 January 2014; Published 16 March 2014
Academic Editor: Maria Gandarias
Copyright © 2014 Igor Leite Freire and Mariano Torrisi. 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.
- L. T. Takahashi, N. A. Maidana, W. Castro Ferreira, Jr., P. Pulino, and H. M. Yang, “Mathematical models for the Aedes aegypti dispersal dynamics: travelling waves by wing and wind,” Bulletin of Mathematical Biology, vol. 67, no. 3, pp. 509–528, 2005.
- I. L. Freire and M. Torrisi, “Symmetry methods in mathematical modeling of Aedes aegypti dispersal dynamics,” Nonlinear Analysis. Real World Applications, vol. 14, no. 3, pp. 1300–1307, 2013.
- I. L. Freire and M. Torrisi, “Transformações de equivalência fracas para uma classe de modelos em biomatemática,” in Anais do Congresso de Matemática Aplicada e Computacional (CMAC-CO '13), 2013.
- I. L. Freire and M. Torrisi, “Similarity solutions for systems arising from an Aedes aegypti model,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 4, pp. 872–879, 2014.
- N. H. Ibragimov, M. Torrisi, and A. Valenti, “Preliminary group classification of equations ,” Journal of Mathematical Physics, vol. 32, no. 11, pp. 2988–2995, 1991.
- I. Lisle, Equivalence transformations for classes of differential equations [Ph.D. thesis], University of British Columbia, 1992.
- M. Senthilvelan, M. Torrisi, and A. Valenti, “Equivalence transformations and differential invariants of a generalized nonlinear Schrödinger equation,” Journal of Physics A, vol. 39, no. 14, pp. 3703–3713, 2006.
- M. L. Gandarias, M. Torrisi, and R. Tracinà, “On some differential invariants for a family of diffusion equations,” Journal of Physics A, vol. 40, no. 30, pp. 8803–8813, 2007.
- J.-P. Gazeau and P. Winternitz, “Symmetries of variable coefficient Korteweg-de Vries equations,” Journal of Mathematical Physics, vol. 33, no. 12, pp. 4087–4102, 1992.
- P. Winternitz and J.-P. Gazeau, “Allowed transformations and symmetry classes of variable coefficient Korteweg-de Vries equations,” Physics Letters A, vol. 167, no. 3, pp. 246–250, 1992.
- L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, NY, USA, 1982.
- I. S. Akhatov, R. K. Gazizov, and N. K. Ibragimov, “Nonlocal symmetries. Heuristic approach,” Journal of Soviet Mathematics, vol. 55, no. 1, pp. 1401–1450, 1991.
- M. Torrisi and R. Tracinà, “Equivalence transformations and symmetries for a heat conduction model,” International Journal of Non-Linear Mechanics, vol. 33, no. 3, pp. 473–487, 1998.
- V. Romano and M. Torrisi, “Application of weak equivalence transformations to a group analysis of a drift-diffusion model,” Journal of Physics A, vol. 32, no. 45, pp. 7953–7963, 1999.
- N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, CRC Press, Boca Raton, Fla, USA, 1996.
- M. Molati and C. M. Khalique, “Lie group classification of a generalized Lane-Emden type system in two dimensions,” Journal of Applied Mathematics, vol. 2012, Article ID 405978, 10 pages, 2012.
- C. M. Khalique, F. M. Mahomed, and B. P. Ntsime, “Group classification of the generalized Emden-Fowler-type equation,” Nonlinear Analysis. Real World Applications, vol. 10, no. 6, pp. 3387–3395, 2009.
- M. Torrisi and R. Tracina, “Equivalence transformations for systems of first order quasilinear partial differential equations,” in Modern Group Analysis VI: Developments in Theory, Computation and Application, N. H. Ibragimov and F. M. Mahomed, Eds., New Age International, 1996.
- M. Torrisi, R. Tracinà, and A. Valenti, “A group analysis approach for a nonlinear differential system arising in diffusion phenomena,” Journal of Mathematical Physics, vol. 37, no. 9, pp. 4758–4767, 1996.
- M. Torrisi and R. Tracinà, “Exact solutions of a reaction-diffusion systems for Proteus mirabilis bacterial colonies,” Nonlinear Analysis. Real World Applications, vol. 12, no. 3, pp. 1865–1874, 2011.
- G. Gambino, A. M. Greco, and M. C. Lombardo, “A group analysis via weak equivalence transformations for a model of tumour encapsulation,” Journal of Physics A, vol. 37, no. 12, pp. 3835–3846, 2004.
- N. H. Ibragimov and N. Säfström, “The equivalence group and invariant solutions of a tumour growth model,” Communications in Nonlinear Science and Numerical Simulation, vol. 9, no. 1, pp. 61–68, 2004.
- M. Torrisi and R. Tracinà, “Second-order differential invariants of a family of diffusion equations,” Journal of Physics A, vol. 38, no. 34, pp. 7519–7526, 2005.
- M. Torrisi and R. Tracinà, “On a class ofd reaction diffusion systems: E quivalence transformations and symmetries,” in Asymptotic Methods in Nonlinear Wave Phenomena, T. Ruggeri and M. Sammartino, Eds., pp. 207–216, 2007.
- N. H. Ibragimov and M. Torrisi, “A simple method for group analysis and its application to a model of detonation,” Journal of Mathematical Physics, vol. 33, no. 11, pp. 3931–3937, 1992.