Classification of cubic polynomials in the nonlinear method of angular boundary functions
https://doi.org/10.22405/2226-8383-2025-26-4-288-301
Abstract
Nonlinear singularly perturbed parabolic equations in domains with angular boundary points are considered. The nonlinear method of angular boundary functions is used to construct the
asymptotics of the solution. It is assumed that in problems determining the main terms of the angular part of the asymptotics of the solution, the nonlinearities are cubic polynomials. The existence of solutions to these problems is based on the method of upper and lower barriers, the construction of which is the main difficulty. In particular, this difficulty is related to the diversity of behavior of cubic polynomials. The paper proposes a classification based on the
allocation of intervals of a certain nature of monotonicity and direction of convexity.
About the Authors
Alexey Igorevich Denisov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
postgraduate student
Igor Vasil’evich Denisov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
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Review
For citations:
Denisov A.I., Denisov I.V. Classification of cubic polynomials in the nonlinear method of angular boundary functions. Chebyshevskii Sbornik. 2025;26(4):288-301. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-288-301
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