Properties of solutions to parabolic equations using the method of angular boundary functions
https://doi.org/10.22405/2226-8383-2026-27-2-162-170
Abstract
Singularly perturbed parabolic equations in domains with corner points of the boundary are considered. The method of corner boundary functions is used to construct the asymptotics of the solution. The purpose of this work is to identify the features of parabolic equations for which the method of corner boundary functions can be applied.
About the Author
Igor Vasil’evich Denisov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Vasilyeva, A.B. & Butuzov, V.F. 1990, Asymptotic methods in the theory of singular perturbations, Vysshaya Shkola, Moscow.
2. Denisov, I.V. 2017, “Angular boundary layer in boundary value problems for singularly perturbed parabolic equations with quadratic nonlinearity”, Computational Mathematics and Mathematical Physics, vol. 57, no. 2, pp. 253–271.
3. Denisov, A.I. & Denisov, I.V. 2019, “Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with nonmonotonic nonlinearities”, Computational Mathematics and Mathematical Physics, vol. 59, no. 9, pp. 1518–1527.
4. Denisov, A.I. & Denisov, I.V. 2025, “Construction of barriers for singularly perturbed parabolic problems with cubic nonlinearities, taking into account the inflection point”, Computational Mathematics and Mathematical Physics, vol. 65, no. 12, pp. 2928–2937.
5. Denisov, I.V. 2021, “Corner boundary layer in boundary value problems with nonlinearities having stationary points”, Computational Mathematics and Mathematical Physics, vol. 61, no. 11, pp. 1855–1863.
6. Denisov, A.I. & Denisov, I.V. 2023, “Nonlinear method of angular boundary functions in problems with cubic nonlinearities”, Chebyshevskii Sbornik, vol. 24, no. 1, pp. 27–39.
7. Denisov, A.I. & Denisov, I.V. 2025, “Nonlinear method of corner boundary functions with the influence of an inflection point”, Computational Mathematics and Mathematical Physics, vol. 65, no. 1, pp. 76–88.
8. Denisov, A.I. & Denisov, I.V. 2025, “Classification of cubic polynomials in the nonlinear method of angular boundary functions”, Chebyshevskii Sbornik, vol. 26, no. 4, pp. 287–300.
Review
For citations:
Denisov I.V. Properties of solutions to parabolic equations using the method of angular boundary functions. Chebyshevskii Sbornik. 2026;27(2):162-170. (In Russ.) https://doi.org/10.22405/2226-8383-2026-27-2-162-170
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