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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN En Línea: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v50.i8.60
pages 66-76

Method of Composition for Systems with Distributed Parameters

Victor G. Bondarenko
National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", Kiev


The method for solving the Cauchy problem of reaction-diffusion equations, which is a nonlinear version of the Trotter–Daletskiy formula, has been justified. The proposed method of composition contributes to the selection of an adequate mathematical model for an object with distributed parameters.


  1. Svirezhev Yu.M., Nonlinear waves, dissipative structures and catastrophes in ecology [in Russian], Nauka, Moscow, 1987.

  2. Murray J.D., Mathematical Biology, Springer-Verlag, New York, 2002, 1, 2.

  3. Conway E., Smoller J., A comparison technique for systems of reaction-diffusion equations, Communications in Partial Differential Equations, 1977, 2 (7), 679–697.

  4. Henry D., Geometric theory of semilinear parabolic equations [Russian translation], Mir, Moscow, 1985.

  5. Аmаnn Н., Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems, Differential Integral Equations, 1990, 3, No. 1, 13–75.

  6. Medvinskiy A.B., Petrovskiy S.V., Tikhonova I.A., Tikhonov D.A. et al., Formation of spatio-temporal structures, fractals and chaos in conceptual ecological models on the example of the dynamics of interacting populations of plankton and fish, Uspekhi Fizicheskikh Nauk, 2002, 172, No. 1, 31–66.

  7. Medvinskiy A.B.,. Petrovskiy S.V., Tikhonova I.A., Malchow H., Spatiotemporal complexity of plankton and fish dynamics, SIAM Review, 2002, 44, No. 3, 311–370.

  8. Trotter T.F., Of the product of semigroups of operators, Pros. Am. Math. Soc., 1959, 10, 545–551.

  9. Daletskiy Yu.L., Continuum integrals associated with operator evolution equations, Uspekhi Matematicheskikh Nauk, 1962, 17, No. 5, 3–115.

  10. Goldstein J., Semigroups of linear operators and their applications [in Russian], Vyshcha shkola, Kiev, 1989.

  11. Taylor М.Е., Partial differential equations III, Springer–Verlag, New York, 1997.

  12. Aronson D.G., Weinberger H.F., Multidimensional nonlinear diffusion arising in population, Advances Mathematics, 1978, 30, 33–76.

  13. Bondarenko V.G., Prokopenko Yu.Yu., Barrier functions for a class of semilinear parabolic equations, Ukrainskiy matematicheskiy zhurnal, 2008, 60, No. 11, 1449–1456.

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