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.
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References
A. A. Dorodnitsyn, “Asymptotic Solution of the Van der Pol Equation,” Prikl. Mat. Mekh. 11, 313–328 (1947).
A. B. Vasil’eva and V. F. Butuzov, Asymptotic Methods in the Theory of Singular Perturbations (Vysshaya Shkola, Moscow, 1990) [in Russian].
C. V. Pao, Nonlinear Parabolic and Elliptic Equations (Plenum, New York, 1992).
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Dedicated to Academician A.A. Dorodnicyn on the Occasion of the Centenary of His Birth
Original Russian Text © V.F. Butuzov, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 1, pp. 44–55.
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Butuzov, V.F. On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation. Comput. Math. and Math. Phys. 51, 40–50 (2011). https://doi.org/10.1134/S0965542511010064
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DOI: https://doi.org/10.1134/S0965542511010064