- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 172654, 8 pages
Nonstationary Fronts in the Singularly Perturbed Power-Society Model
1Institute of System Analysis of RAS, Higher School of Economics, Moscow 101000, Russia
2Russian State Social University, Moscow 129226, Russia
3Keldysh Institute of Applied Mathematics RAS, Moscow 125047, Russia
Received 23 July 2013; Accepted 15 September 2013
Academic Editor: Allaberen Ashyralyev
Copyright © 2013 M. G. Dmitriev et al. 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.
- V. F. Butuzov and A. B. Vasil’eva, “Asymptotic behavior of a solution of contrasting structure type,” Akademiya Nauk SSSR, vol. 42, no. 6, pp. 831–841, 1987.
- V. F. Butuzov, A. B. Vasil’eva, and N. N. Nefedov, “Asymptotic theory of contrasting structures. A survey,” Automation and Remote Control, vol. 58, no. 7, pp. 1068–1091, 1997.
- A. B. Vasil’eva, V. F. Butuzov, and N. N. Nefedov, “Singularly perturbed problems with boundary and internal layers,” Proceedings of the Steklov Institute of Mathematics, vol. 268, no. 1, pp. 258–273, 2010.
- A. B. Vasil’eva, V. F. Butuzov, and N. N. Nefëdov, “Contrast structures in singularly perturbed problems,” Fundamental'naya i Prikladnaya Matematika, vol. 4, no. 3, pp. 799–851, 1998.
- Yu. V. Bozhevol’nov and N. N. Nefëdov, “Front motion in a parabolic reaction-diffusion problem,” Computational Mathematics and Mathematical Physics, vol. 50, no. 2, pp. 264–273, 2010.
- A. Vasil’eva, A. Nikitin, and A. Petrov, “Stability of contrasting solutions of nonlinear hydromagnetic dynamo equations and magnetic fields reversals in galaxies,” Geophysical and Astrophysical Fluid Dynamics, vol. 78, no. 1–4, pp. 261–279, 1994.
- D. Moss, A. Petrov, and D. Sokoloff, “The motion of magnetic fronts in spiral galaxies,” Geophysical and Astrophysical Fluid Dynamics, vol. 92, no. 1-2, pp. 129–149, 2000.
- A. B. Vasil’eva, A. P. Petrov, and À. À. Plotnikov, “Alternating contrast structures,” Computational Mathematics and Mathematical Physics, vol. 38, no. 9, pp. 1471–1480, 1998.
- A. P. Mikhailov, “Mathematical modeling of the authority in the hierarchical structures,” Mathematical Modeling, vol. 6, article 6, 1994 (Russian).
- A. A. Samarskii and A. P. Mikhailov, Principles of mathematical modeling, Ideas, methods, examples, vol. 3 of Numerical Insights, Taylor & Francis, London, UK, 2002.
- A. P. Mikhailov, “Mathematical modeling of power distribution in state ierarchical structures interacting with civil society,” in Proceedings of 14th IMACS World Congress, vol. 2, p. 828, Atlanta, Ga, USA, 1994.
- A. P. Mikhailov, “The research of the “Power-Society” system,” Fizmatlit, 2006, (in Russian).
- V. F. Butuzov and I. V. Nedelko, “On the global influence domain of stable solutions with internal layers,” Differential Equations, vol. 192, no. 5, pp. 13–52, 2001.
- N. N. Nefëdov and A. G. Nikitin, “The method of differential inequalities for step-type contrast structures in singularly perturbed integro-differential equations in the spatially two-dimensional case,” Differential Equations, vol. 42, no. 5, pp. 739–749, 2006.
- N. N. Nefedov, A. G. Nikitin, M. A. Petrova, and L. Rekke, “Moving fronts in integro-parabolic reaction-advection-diffusion equations,” Differential Equations, vol. 47, no. 9, pp. 1318–1332, 2011.
- N. N. Nefëdov and A. G. Nikitin, “Boundary and internal layers in the reaction-diffusion problem with a nonlocal inhibitor,” Computational Mathematics and Mathematical Physics, vol. 51, no. 6, pp. 1011–1019, 2011.
- M. Dmitriev, A. Petrov, and G. Zhukova, “The nonlinear “Authority-Society” model,” WSEAS Transactions on Mathematics, vol. 2, no. 1-2, pp. 31–36, 2003.
- A. B. Vasil’eva and V. F. Butuzov, “The method of boundary layer functions,” Differential Equations, vol. 21, no. 10, pp. 1107–1112, 1985.
- M. G. Dmitriev, A. A. Pavlov, and A. P. Petrov, “Optimal power volume in social-economical hierarchy by consumption per capita criterion,” Informacionnye Technologii i Vychislitelnye Sistemy, vol. 4, pp. 4–11, 2007 (Russian).