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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 4, Pages 615–623 (Mi zvmmf484)  

This article is cited in 19 scientific papers (total in 19 papers)

Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations

V. T. Volkov, N. N. Nefedov

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: The asymptotical method of differential inequalities is developed for a new class of periodic problems of reaction-diffusion type. The problem of the existence and Lyapunov stability of periodic solutions with internal transient layers in the case of balanced nonlinearity is studied.

Key words: singular perturbations, reaction-diffusion, contrast structures, internal layers.

Full text: PDF file (990 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:4, 585–593

Bibliographic databases:

UDC: 519.633
Received: 31.10.2005

Citation: V. T. Volkov, N. N. Nefedov, “Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 615–623; Comput. Math. Math. Phys., 46:4 (2006), 585–593

Citation in format AMSBIB
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\paper Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations
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\transl
\jour Comput. Math. Math. Phys.
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nefedov N.N., Recke L., Schneider K.R., “Asymptotic stability via the Krein-Rutman theorem for singularly perturbed parabolic periodic Dirichlet problems”, Regul. Chaotic Dyn., 15:2-3 (2010), 382–389  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. N. T. Levashova, N. N. Nefedov, A. V. Yagremtsev, “Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection”, Comput. Math. Math. Phys., 53:3 (2013), 273–283  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Nefedov N.N., Recke L., Schneider K.R., “Existence and Asymptotic Stability of Periodic Solutions with an Interior Layer of Reaction-Advection-Diffusion Equations”, J. Math. Anal. Appl., 405:1 (2013), 90–103  crossref  mathscinet  zmath  isi  elib  scopus
    4. Zhu Y.-F. Ren Y.-Sh. Dai Q.-Y., “Dynamic Simulation of Nonlinear Vibration on Large Horizontal Axis Turbine Blades Using a Finite Differential Method”, J. Vibroeng., 15:4 (2013), 1991–2002  isi  elib
    5. Butuzov V.F. Nefedov N.N. Recke L. Schneider K.R., “Periodic Solutions With a Boundary Layer of Reaction-Diffusion Equations With Singularly Perturbed Neumann Boundary Conditions”, Int. J. Bifurcation Chaos, 24:8 (2014), 1440019  crossref  mathscinet  zmath  isi  elib  scopus
    6. Levashova N.T. Nikolaeva O.A. Pashkin A.D., “Simulation of the Temperature Distribution At the Water-Air Interface Using the Theory of Contrast Structures”, Mosc. Univ. Phys. Bull., 70:5 (2015), 341–345  crossref  mathscinet  isi  elib  scopus
    7. Nefedov N.N. Nikulin E.I., “Existence and Stability of Periodic Contrast Structures in the Reaction-Advection-Diffusion Problem”, Russ. J. Math. Phys., 22:2 (2015), 215–226  crossref  mathscinet  zmath  isi  elib  scopus
    8. N. T. Levashova, A. A. Melnikova, S. V. Bytsyura, “Primenenie metoda differentsialnykh neravenstv dlya obosnovaniya resheniya sistemy parabolicheskikh uravnenii v vide dvizhuschegosya fronta”, Model. i analiz inform. sistem, 23:3 (2016), 317–325  mathnet  crossref  mathscinet  elib
    9. D. V. Lukyanenko, V. T. Volkov, N. N. Nefedov, L. Recke, K. Schneider, “Analytic-numerical approach to solving singularly perturbed parabolic equations with the use of dynamic adapted meshes”, Model. i analiz inform. sistem, 23:3 (2016), 334–341  mathnet  crossref  mathscinet  elib
    10. N. N. Nefedov, E. I. Nikulin, “Existence and stability of periodic solutions for reaction-diffusion equations in the two-dimensional case”, Model. i analiz inform. sistem, 23:3 (2016), 342–348  mathnet  crossref  mathscinet  elib
    11. E. A. Antipov, V. T. Volkov, N. T. Levashova, N. N. Nefedov, “Reshenie vida dvizhuschegosya fronta dvumernoi zadachi reaktsiya-diffuziya”, Model. i analiz inform. sistem, 24:3 (2017), 259–279  mathnet  crossref  elib
    12. Lukyanenko D., Nefedov N., Nikulin E., Volkov V., “Use of Asymptotics For New Dynamic Adapted Mesh Construction For Periodic Solutions With An Interior Layer of Reaction-Diffusion-Advection Equations”, Numerical Analysis and Its Applications (NAA 2016), Lecture Notes in Computer Science, 10187, eds. Dimov I., Farago I., Vulkov L., Springer International Publishing Ag, 2017, 107–118  crossref  mathscinet  zmath  isi  scopus
    13. Kvas A.A., Levashova N.T., Salnik A.K., “Using Asymptotic Analysis For Developing a One-Dimensional Substance Transport Model in the Case of Spatial Heterogeneity”, Mosc. Univ. Phys. Bull., 72:6 (2017), 518–526  crossref  isi  scopus
    14. Nefedov N.N. Nikulin E.I., “Existence and Stability of Periodic Contrast Structures in the Reaction-Advection-Diffusion Problem in the Case of a Balanced Nonlinearity”, Differ. Equ., 53:4 (2017), 516–529  crossref  mathscinet  zmath  isi  scopus
    15. Orlov A.O. Levashova N.T. Nefedov N.N., “Solution of Contrast Structure Type For a Parabolic Reaction-Diffusion Problem in a Medium With Discontinuous Characteristics”, Differ. Equ., 54:5 (2018), 669–686  crossref  mathscinet  isi  scopus
    16. N. T. Levashova, N. N. Nefedov, A. V. Yagremtsev, “Existence of a solution in the form of a moving front of a reaction-diffusion-advection problem in the case of balanced advection”, Izv. Math., 82:5 (2018), 984–1005  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. E. A. Antipov, N. T. Levashova, N. N. Nefedov, “Asimptoticheskoe priblizhenie resheniya uravneniya reaktsiya-diffuziya-advektsiya s nelineinym advektivnym slagaemym”, Model. i analiz inform. sistem, 25:1 (2018), 18–32  mathnet  crossref  elib
    18. S. V. Bytsyura, N. T. Levashova, “Verkhnee i nizhnee resheniya dlya sistemy uravnenii tipa FitsKhyu–Nagumo”, Model. i analiz inform. sistem, 25:1 (2018), 33–53  mathnet  crossref  elib
    19. Nefedov N.N. Nikulin E.I. Recke L., “On the Existence and Asymptotic Stability of Periodic Contrast Structures in Quasilinear Reaction-Advection-Diffusion Equations”, Russ. J. Math. Phys., 26:1 (2019), 55–69  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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