Artículos de revistas
Symmetry Analysis Of The Bidimensional Lane-emden Systems
Registro en:
Journal Of Mathematical Analysis And Applications. , v. 388, n. 2, p. 1279 - 1284, 2012.
0022247X
10.1016/j.jmaa.2011.11.024
2-s2.0-84855357578
Autor
Bozhkov Y.
Freire I.L.
Institución
Resumen
We carry out a complete group classification of the nonlinear Lane-Emden systems in dimension two. The Noether symmetries are found and their corresponding conservation laws are established. © 2011 Elsevier Inc. 388 2 1279 1284 Bluman, G.W., Anco, S., (2002) Symmetry and Integration Methods for Differential Equations, , Springer, New York Bluman, G.W., Kumei, S., Symmetries and Differential Equations (1989) Appl. Math. Sci., 81. , Springer, New York Bozhkov, Y., Martins, A.C.G., Lie point symmetries of the Lane-Emden systems (2004) J. Math. Anal. Appl., 294, pp. 334-344 Bozhkov, Y., Freire, I.L., Special conformal groups of a Riemannian manifold and the Lie point symmetries of the nonlinear Poisson equations (2010) J. Differential Equations, 249, pp. 872-913 Bozhkov, Y., Mitidieri, E., Lie symmetries and criticality of semilinear differential systems (2007) SIGMA Symmetry Integrability Geom. Methods Appl., 3, p. 17. , Paper 053 Bozhkov, Y., Olver, P.J., Pohozhaev and Morawetz identities in elastostatics and elastodynamics (2011) SIGMA Symmetry Integrability Geom. Methods Appl., 7, p. 9. , Paper 055 Busca, J., Manasevich, R., A Liouville type theorem for the Lane-Emden systems (2002) Indiana Univ. Math. J., 51, pp. 37-51 Cantwell, B.J., Introduction to Symmetry Analysis (2002) Cambridge Texts Appl. Math., , Cambridge Univ. Press Ghergu, M., Lane-Emden systems with negative exponents (2010) J. Funct. Anal., 258, pp. 3295-3318 Gidas, B., Spruck, J., Global and local behaviour of positive solutions of nonlinear elliptic equations (1981) Comm. Pure Appl. Math., 34, pp. 525-598 Hulshof, J., van der Vorst, R.C.A.M., Asymptotic behavior of ground states (1996) Proc. Amer. Math. Soc., 124, pp. 2423-2431 Ibragimov, N.H., Transformation Groups Applied to Mathematical Physics (1985) Math. Appl. (Soviet Ser.), , D. Reidel Publishing Co., Dordrecht, translated from Russian Lions, P.L., The concentration-compactness principle in the calculus of variations, part 1 (1985) Rev. Mat. Iberoam., 1, pp. 145-201 Mitidieri, E., A Relich type identity and applications (1993) Comm. Partial Differential Equations, 18 (1-2), pp. 125-151 Mitidieri, E., Nonexistence of positive solutions of semilinear elliptic systems in R N (1996) Differential Integral Equations, 9, pp. 465-479 Muatjetjeja, B., Khalique, C.M., Lagrangian approach to a generalized coupled Lane-Emden system: symmetries and first integrals (2010) Commun. Nonlinear Sci. Numer. Simul., 15, pp. 1166-1171 Muatjetjeja, B., Khalique, C.M., Noether, partial Noether operators and first integrals for the coupled Lane-Emden system (2010) Math. Comput. Appl., 15, pp. 325-333 Muatjetjeja, B., Khalique, C.M., First integrals for a generalized coupled Lane-Emden system (2011) Nonlinear Anal. Real World Appl., 12, pp. 1202-1212 Naz, R., Mahomed, F.M., Mason, D.P., Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics (2008) Appl. Math. Comput., 205, pp. 212-230 Noether, E., Invariante Variationsprobleme (1971) Nachr. Akad. Wiss. Gottingen Math.-Phys. Kl.. Transport Theory Statist. Phys., 1 (3), pp. 186-207. , English translation in: Olver, P.J., (1986) Applications of Lie Groups to Differential Equations, , Springer, New York Popovych, R.O., Ivanova, N.M., Hierarchy of conservation laws of diffusion-convection equations (2005) J. Math. Phys., 46, p. 043502. , 22 pp Serrin, J., Zou, H., Non-existence of positive solutions of semilinear elliptic systems (1994), 3, pp. 55-68. , in: Discourses in Mathematics and Its Applications, Department of Mathematics, Texas A&M University, College Station, TXSerrin, J., Zou, H., Non-existence of positive solutions of the Lane-Emden systems (1996) Differential Integral Equations, 9, pp. 635-653 Serrin, J., Zou, H., Existence of positive solutions of the Lane-Emden systems (1998) Atti Semin. Mat. Fis. Univ. Modena, 46 (SUPPL.), pp. 369-380 Svirshchevskii, S.R., Group classification of nonlinear polyharmonic equations and their invariant solutions (1993) Differ. Equ.. Differ. Uravn., 29, pp. 1772-1781. , (in Russian) Zhang, Z., Positive solutions of Lane-Emden systems with negative exponents: existence, boundary behavior and uniqueness (2011) Nonlinear Anal., 74, pp. 5544-5553 Zou, H., Symmetry of ground states for a semilinear elliptic system (1999) Trans. Amer. Math. Soc., 352, pp. 1217-1245