Theoretical Foundations of Chemical Engineering

, Volume 49, Issue 5, pp 622–635

Exact solutions and qualitative features of nonlinear hyperbolic reaction—diffusion equations with delay

Article

DOI: 10.1134/S0040579515050243

Cite this article as:
Polyanin, A.D., Sorokin, V.G. & Vyazmin, A.V. Theor Found Chem Eng (2015) 49: 622. doi:10.1134/S0040579515050243

Abstract

New classes of exact solutions to nonlinear hyperbolic reaction—diffusion equations with delay are described. All of the equations under consideration depend on one or two arbitrary functions of one argument, and the derived solutions contain free parameters (in certain cases, there can be any number of these parameters). The following solutions are found: periodic solutions with respect to time and space variable, solutions that describe the nonlinear interaction between a standing wave and a traveling wave, and certain other solutions. Exact solutions are also presented for more complex nonlinear equations in which delay arbitrarily depends on time. Conditions for the global instability of solutions to a number of reaction—diffusion systems with delay are derived. The generalized Stokes problem subject to the periodic boundary condition, which is described by a linear diffusion equation with delay, is solved.

Keywords

nonlinear reaction–diffusion equations with delay exact solutions generalized separable solutions functional separable solutions delay differential equations global instability of solutions generalized Stokes problem 

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • A. D. Polyanin
    • 1
    • 2
  • V. G. Sorokin
    • 3
  • A. V. Vyazmin
    • 4
  1. 1.Ishlinskii Institute for Problems in MechanicsRussian Academy of SciencesMoscowRussia
  2. 2.National Research Nuclear University MEPhIMoscowRussia
  3. 3.Bauman Moscow State Technical UniversityMoscowRussia
  4. 4.Environmental and Chemical Engineering InstituteMoscow State University of Mechanical EngineeringMoscowRussia

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