Simulation of the temperature distribution at the water–air interface using the theory of contrast structures

Левашова, Н. Т.; Nikolaeva, O. A.; Pashkin, Artem

doi:10.3103/s0027134915050082

Cited by 14 publications

(5 citation statements)

References 5 publications

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“…The function ϵ 2 k ( x ) is the thermal diffusivity coefficient. The experimental data shows that this function undergoes a discontinuity of the first kind at the media interface; thus, we set

k (x) = \{\begin{matrix} 1, x \in false[- 1; 0 false], \\ 4, x \in false[0; 1 false] . \end{matrix} f (u, x) = \{\begin{matrix} u - U_{w}, x \in false[- 1; 0 false], \\ u - U_{a}, x \in false[0; 1 false] . \end{matrix}

The conditions Assumption and are obviously valid for problem , φ ( − ) = U w , φ ( + ) = U a .…”

Section: Examplementioning

confidence: 99%

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The solution with internal transition layer of the reaction‐diffusion equation in case of discontinuous reactive and diffusive terms

Левашова

Нефедов

Nikolaeva

et al. 2018

Math Methods in App Sciences

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In this paper, we use the asymptotical analysis to construct the asymptotic approximation of the solution with internal transition layer of the boundary value problem for a reaction-diffusion equation on the segment in case of discontinuous reactive and diffusive terms. The internal layer is located in the vicinity of a single point of discontinuity of the mentioned terms. We also investigate the existence and stability of such solution. For the last purpose, we use the asymptotical method of differential inequalities. KEYWORDS asymptotic approximation, discontinuous terms, lower and upper solutions, reaction-diffusion problem, small parameter Math Meth Appl Sci. 2018;41:9203-9217.wileyonlinelibrary.com/journal/mma

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“…The function ϵ 2 k ( x ) is the thermal diffusivity coefficient. The experimental data shows that this function undergoes a discontinuity of the first kind at the media interface; thus, we set

k (x) = \{\begin{matrix} 1, x \in false[- 1; 0 false], \\ 4, x \in false[0; 1 false] . \end{matrix} f (u, x) = \{\begin{matrix} u - U_{w}, x \in false[- 1; 0 false], \\ u - U_{a}, x \in false[0; 1 false] . \end{matrix}

The conditions Assumption and are obviously valid for problem , φ ( − ) = U w , φ ( + ) = U a .…”

Section: Examplementioning

confidence: 99%

“…Boundary value problems with internal transition layers are appropriate for modeling of physical phenomena at the bounds of various spatial inhomogenities. One of such problems is simulation of temperature at the water‐air interface . In last case, the reactive term and the diffusion coefficient occur to be discontinuous.…”

Section: Introductionmentioning

confidence: 99%

The solution with internal transition layer of the reaction‐diffusion equation in case of discontinuous reactive and diffusive terms

Левашова

Нефедов

Nikolaeva

et al. 2018

Math Methods in App Sciences

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“…The first of these conditions follows from the condition in (6) and 7which the transition layer terms in the series Q (−) (τ, t, ) vanish in the neighborhood of the line…”

Section: Q (∓)mentioning

confidence: 99%

“…Reaction-diffusion equations with boundary value are important in mathematical model and these boundary value problems with internal transition layer have many applications in different areas such as chemical and biological kinetics, physical phenomenon, population dynamics and so on [20]. The interest in reaction-diffusion equations with discontinuous reactive functions is highlight because of the development of some mathematical models which describe the phenomena on various media interfaces such as the temperature on the water-air interface [6] and the distribution of wave functions of carriers in layered superconductor structures [18]. In order to describe these model, we need to use equations with small parameters multiplying the derivatives with respect to spatial coordinates, which is known as singularly perturbed equations [12,7].…”

mentioning

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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Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms

2020

Communications in Nonlinear Science and Numerical Simulation

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Simulation of the temperature distribution at the water–air interface using the theory of contrast structures

Cited by 14 publications

References 5 publications

The solution with internal transition layer of the reaction‐diffusion equation in case of discontinuous reactive and diffusive terms

The solution with internal transition layer of the reaction‐diffusion equation in case of discontinuous reactive and diffusive terms

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

Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms

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