Publication de 12 numéros par an
ISSN Imprimer: 1064-2315
ISSN En ligne: 2163-9337
Indexed in
Method of Composition for Systems with Distributed Parameters
RÉSUMÉ
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.
-
Svirezhev Yu.M., Nonlinear waves, dissipative structures and catastrophes in ecology [in Russian], Nauka, Moscow, 1987.
-
Murray J.D., Mathematical Biology, Springer-Verlag, New York, 2002, 1, 2.
-
Conway E., Smoller J., A comparison technique for systems of reaction-diffusion equations, Communications in Partial Differential Equations, 1977, 2 (7), 679–697.
-
Henry D., Geometric theory of semilinear parabolic equations [Russian translation], Mir, Moscow, 1985.
-
Аmаnn Н., Dynamic theory of quasilinear parabolic equations. II. Reaction-diffusion systems, Differential Integral Equations, 1990, 3, No. 1, 13–75.
-
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.
-
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.
-
Trotter T.F., Of the product of semigroups of operators, Pros. Am. Math. Soc., 1959, 10, 545–551.
-
Daletskiy Yu.L., Continuum integrals associated with operator evolution equations, Uspekhi Matematicheskikh Nauk, 1962, 17, No. 5, 3–115.
-
Goldstein J., Semigroups of linear operators and their applications [in Russian], Vyshcha shkola, Kiev, 1989.
-
Taylor М.Е., Partial differential equations III, Springer–Verlag, New York, 1997.
-
Aronson D.G., Weinberger H.F., Multidimensional nonlinear diffusion arising in population, Advances Mathematics, 1978, 30, 33–76.
-
Bondarenko V.G., Prokopenko Yu.Yu., Barrier functions for a class of semilinear parabolic equations, Ukrainskiy matematicheskiy zhurnal, 2008, 60, No. 11, 1449–1456.