Abstract:
For singularly perturbed parabolic problems, asymptotic expansions of time-periodic solutions with boundary layers in a neighborhood of interval's endpoints are constructed and justified in the case where the degenerate equation has a double or a triple root.
Key words:singularly perturbed parabolic equations, asymptotic boundary layer, multiple roots of the degenerate equation.
Citation:
V. F. Butuzov, “On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation”, Zh. Vychisl. Mat. Mat. Fiz., 51:1 (2011), 44–55; Comput. Math. Math. Phys., 51:1 (2011), 40–50
\Bibitem{But11}
\by V.~F.~Butuzov
\paper On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2011
\vol 51
\issue 1
\pages 44--55
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\transl
\jour Comput. Math. Math. Phys.
\yr 2011
\vol 51
\issue 1
\pages 40--50
\crossref{https://doi.org/10.1134/S0965542511010064}
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Linking options:
https://www.mathnet.ru/eng/zvmmf8045
https://www.mathnet.ru/eng/zvmmf/v51/i1/p44
This publication is cited in the following 22 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, “Multiscale study on a class of singularly perturbed system with discontinuous right-hand side and multiple root of the degenerate solution”, Communications in Nonlinear Science and Numerical Simulation, 139 (2024), 108247
Yang Q., Ni M., “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), 291–308
G. A. Kurina, M. A. Kalashnikova, “Singularly perturbed problems with multi-tempo fast variables”, Autom. Remote Control, 83:11 (2022), 1679–1723
Galina Bizhanova, “Solution of the nonregular problem for a parabolic equation with the time derivative in the boundary condition”, ASY, 130:1-2 (2022), 53
Q. Yang, M. Ni, “Multizonal boundary and internal layers in the singularly perturbed problems for a stationary equation of reaction–advection–diffusion type with weak and discontinuous nonlinearity”, Comput. Math. Math. Phys., 62:12 (2022), 2123–2138
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
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
A. A. Bykov, K. E. Ermakova, “Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium”, Math. Models Comput. Simul., 12:3 (2020), 329–347
Butuzov V.F., “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
A. A. Bykov, K. E. Ermakova, “Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order”, Comput. Math. Math. Phys., 58:12 (2018), 1977–1988
Bykov A.A. Ermakova K.E., “Exact Solutions of the Equations of a Nonstationary Front With Equilibrium Points of An Infinite Order of Degeneracy”, Mosc. Univ. Phys. Bull., 73:6 (2018), 583–591
A. A. Bykov, K. E. Ermakova, “Resheniya uravnenii nestatsionarnogo fronta reaktsii s vyrozhdennymi tochkami ravnovesiya”, Model. i analiz inform. sistem, 24:3 (2017), 309–321
Butuzov V.F., Nefedov N.N., Recke L., Schneider K.R., “Asymptotics, Stability, and Region of Attraction of Periodic Solution to a Singularly Perturbed Parabolic Problem With Double Root of a Degenerate Equation”, Autom. Control Comp. Sci., 51:7 (2017), 606–613
V. F. Butuzov, N. N. Nefedov, L. Recke, K. Schneider, “Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation”, Automatic Control and Computer Sciences, 51:7 (2017), 606–613
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
V. F. Butuzov, “Singularly perturbed boundary value problem with multizonal interior transitional layer”, Automatic Control and Computer Sciences, 49:7 (2015), 493–507
V. F. Butuzov, “On the Special Properties of the Boundary Layer in Singularly Perturbed Problems with Multiple Root of the Degenerate Equation”, Math. Notes, 94:1 (2013), 60–70