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Initial boundary value problem analyzes the solution's uniformity in a rectangle, implying significant findings in nonlinear dynamics.
An initial boundary value problem for singularly perturbed parabolic equations with cubic nonlinearities is considered in a rectangle. The inflection point of the cubic parabola is assumed to be located to the left of the root of the degenerate equation. The nonlinear method of angular parabolic functions is used to construct a complete asymptotic expansion of the solution to the problem and prove its uniformity in a closed rectangle with respect to a small parameter. This work completes the study of singularly perturbed parabolic problems with cubic nonlinearities.
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A.I. Denisov (2025) studied this question.
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