Internal Layer for a System of Singularly Perturbed Equations with Discontinuous Right-Hand Side

Pang, Yafei; Ni, Mingkang; Левашова, Н. Т.

doi:10.1134/s0012266118120054

Cited by 9 publications

(2 citation statements)

References 9 publications

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“…i (+∞, t) = 0, (27) where the functions Qf j (τ, t), j < i. The solutions of problem (27) are expressed in explicit form:…”

Section: 3mentioning

confidence: 99%

“…In [25], Pan, Ni and Levashova constructed the asymptotic expansion and proved the existence of a solution with an internal transition layer of a singular perturbed boundary value problem for a second-order quasi-linear ordinary differential equation in which the nonlinearity is discontinuous. Moreover, Pan, Ni and Levashova studied a system of two singularly perturbed first-order equations which have discontinuous right-hand sides and equal powers of the small parameter multiplying the derivatives in [27], and they proved the existence of the solution with internal layer and construct its asymptotic approximation by the boundary function method and the matching method. In [26], Pan, Ni and Davaydova considered a singularly perturbed boundary-value problem for a nonlinear stationary equation of reaction-diffusion-advection type which is weakly dependent on the first order derivative.…”

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confidence: 99%

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Solution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term

Wu¹,

Ni²

2021

DCDS-S

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In this paper, we consider the Dirichlet boundary value problem for a singularly perturbed reaction-diffusion equation with discontinuous reactive term. We use the asymptotic analysis to construct the formal asymptotic approximation of the solution with internal and boundary layers. The internal layer is located in the vicinity of a curve of the discontinuous reactive term. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution and estimate the accuracy of its asymptotic approximation.

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“…i (+∞, t) = 0, (27) where the functions Qf j (τ, t), j < i. The solutions of problem (27) are expressed in explicit form:…”

Section: 3mentioning

confidence: 99%

mentioning

confidence: 99%

Solution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term

Wu¹,

Ni²

2021

DCDS-S

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Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation

Yang

Ni²

2023

Chin. Ann. Math. Ser. B

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Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation

Yang

2021

Sci. China Math.

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A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case where the degenerate equation has a multiple root on the left-hand side of the curve which separates the domain and an isolated root on the right-hand side of that curve. The asymptotics of a solution with an internal layer near a point on the discontinuous curve and the transition point is constructed. The method to construct the internal layer function is proposed. The behavior of the solution in the internal layer consisting of four zones essentially differs from the case of isolated roots. For sufficiently small parameter values, the existence of a smooth solution with an internal layer from the multiple root of the degenerate equation to the isolated root in the neighborhood of a point on the discontinuous curve is proved. The method can be shown to be effective in the given example.

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Internal Layer for a System of Singularly Perturbed Equations with Discontinuous Right-Hand Side

Cited by 9 publications

References 9 publications

Solution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term

Solution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term

Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation

Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation

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