Abstract:
Two-point boundary value problem for a singularly perturbed ordinary differential equation of second order is considered in the case when the degenerate equation has three unintersecting roots from which one root is two-tuple and two roots are one-tuple. It is prooved that for sufficiently small values of the small parameter the problem has a solution with the transition from the two-tuple root of the degenerate equation to the one-tuple root in the neighbourhood of an internal point of the interval. The asymptotic expansion of this solution is constructed. It distinguishes from the known expansion in the case when all roots of the degenerate equation are one-tuple, in particular, the transitional layer is multizonal.
Keywords:singularly perturbed equation, interior transitional layer, asymptotic expansion of solution.
Citation:
V. F. Butuzov, “Singularly perturbed boundary value problem with multizonal interior transitional layer”, Model. Anal. Inform. Sist., 22:1 (2015), 5–22; Automatic Control and Computer Sciences, 49:7 (2015), 493–507
\Bibitem{But15}
\by V.~F.~Butuzov
\paper Singularly perturbed boundary value problem with multizonal interior transitional layer
\jour Model. Anal. Inform. Sist.
\yr 2015
\vol 22
\issue 1
\pages 5--22
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\transl
\jour Automatic Control and Computer Sciences
\yr 2015
\vol 49
\issue 7
\pages 493--507
\crossref{https://doi.org/10.3103/S0146411615070044}
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Linking options:
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This publication is cited in the following 10 articles:
Qian Yang, Mingkang Ni, “Multizonal Internal Layers in a Stationary Piecewise–Smooth Reaction-Diffusion Equation in the Case of the Difference of Multiplicity for the Roots of the Degenerate Solution”, Comput. Math. and Math. Phys., 64:5 (2024), 1130
Qian Yang, Mingkang Ni, “Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation”, Sci. China Math., 65:2 (2022), 291
Qian Yang, Mingkang Ni, “ASYMPTOTICS OF A MULTIZONAL INTERNAL LAYER SOLUTION TO A PIECEWISE-SMOOTH SINGULARLY PERTURBED EQUATION WITH A TRIPLE ROOT OF THE DEGENERATE EQUATION”, jaac, 12:6 (2022), 2441
V. F. Butuzov, “Asymptotics of a steplike contrast structure in a partially dissipative stationary system of equations”, Comput. Math. Math. Phys., 61:1 (2021), 53–79
Mingkang Ni, Qian Yang, “Multizonal internal layers in the singularly perturbed equation with a discontinuous right-hand side”, Comput. Math. Math. Phys., 61:6 (2021), 953–963
V. F. Butuzov, R. E. Simakov, “Asymptotics of the Solution of a Singularly Perturbed System of
Equations with a Multizone Internal Layer”, Diff Equat, 57:4 (2021), 415
V. F. Butuzov, “Asymptotics of a spike type contrast structure in a problem with a multiple root of the degenerate equation”, Differ. Equ., 55:6 (2019), 758–775
V. F. Butuzov, “On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer”, Comput. Math. Math. Phys., 58:6 (2018), 925–949
V. F. Butuzov, “O kontrastnykh strukturakh s mnogozonnym vnutrennim sloem”, Model. i analiz inform. sistem, 24:3 (2017), 288–308
V. F. Butuzov, A. I. Bychkov, “Nachalno-kraevaya zadacha dlya singulyarno vozmuschennogo parabolicheskogo uravneniya v sluchayakh dvukratnogo i trekhkratnogo kornya vyrozhdennogo uravneniya”, Chebyshevskii sb., 16:4 (2015), 41–76