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

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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.

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References

  1. N. N. Nefedov, “An Asymptotic Method of Differential Inequalities for the Investigation of Periodic Contrast Structures: Existence, Asymptotics, and Stability,” Differ. Uravn. 36, 262–269 (2000) [Differ. Equations 36, 298–305 (2000)].

    MATH  MathSciNet  Google Scholar 

  2. A. B. Vasil’eva and O. E. Omel’chenko, “Periodic Step-Like Contrast Structures for a Singularly Perturbed Parabolic Equation,” Differ. Uravn. 36, 209–218 (2000) [Differ. Equations 36, 236–246 (2000)].

    MathSciNet  Google Scholar 

  3. A. B. Vasil’eva, V. F. Butuzov, and N. N. Nefedov, “Contrast Structures in Singularly Perturbed Problems,” Fundament. Prikl. Mat. 4, 799–851 (1998).

    MathSciNet  Google Scholar 

  4. V. T. Volkov and N. N. Nefedov, “On Periodic Solutions Containing Boundary Layers for a Singularly Perturbed Reaction-Diffusion Model,” Zh. Vychisl. Mat. Mat. Fiz. 34, 1307–1315 (1994).

    MathSciNet  Google Scholar 

  5. H. Amman, Periodic Solutions of Semilinear Parabolic Equations in Nonlinear Analysis (Academic, New York, 1978).

    Google Scholar 

  6. N. N. Nefedov, “The Method of Differential Inequalities for Certain Classes of Nonlinear Singularly Perturbed Problems with Internal Layers,” Differ. Uravn. 31, 1142–1149 (1995).

    MATH  MathSciNet  Google Scholar 

  7. C. V. Pao, Nonlinear Parabolic and Elliptic Equations (Plenum, New York; London, 1992).

    Google Scholar 

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Authors and Affiliations

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

    V. T. Volkov & N. N. Nefedov

Authors
  1. V. T. Volkov
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  2. N. N. Nefedov
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Original Russian Text © V.T. Volkov, N.N. Nefedov, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 4, pp. 615–623.

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Volkov, V.T., Nefedov, N.N. Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations. Comput. Math. and Math. Phys. 46, 585–593 (2006). https://doi.org/10.1134/S0965542506040075

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  • DOI: https://doi.org/10.1134/S0965542506040075

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