Numerical Study of Estimating the Blow-Up Time of Positive Solutions of Semilinear Heat Equations

Adou, K. Achille; Touré, Kidjégbo Augustin; Coulibaly, A.

doi:10.17654/am100040291

Cited by 2 publications

(2 citation statements)

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“…By following, it is also proved that when quenching occurs, the semidiscrete quenching time converges to the theoretical one when the mesh size goes to zero and we give a result on numerical non-simultaneous quenching rate. For previous work on numerical approximations of heat equations with non-linear boundary conditions we refer to [1,2,5,[11][12][13]16] and the references cited therein. The rest of the paper is organized as follows : in the next section, we give some properties concerning our semidiscrete scheme.…”

Section: Introductionmentioning

confidence: 99%

Numerical Quenching for Heat Equations with Coupled Nonlinear Boundary Flux

Edja

Koffi

Koua

et al. 2019

ijaa

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In this paper, we study a numerical approximation of the following problem ut = uxx, vt = vxx, 0 < x < 1, 0 < t < T ; ux(0, t) = u −m (0, t) + v −p (0, t), vx(0, t) = u −q (0, t) + v −n (0, t) and ux(1, t) = vx(1, t) = 0, 0 < t < T, where m, p, q and n are parameters. We prove that the solution of a semidiscrete form of above problem quenches in a finite time only at first node of the mesh. We show that the time derivative of the solution blows up at quenching node. Some conditions under which the non-simultaneous or simultaneous quenching occurs for the solution of the semidiscrete problem are obtained. We establish the convergence of the quenching time. Finally, some numerical results to illustrate our analysis are given.

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Section: Introductionmentioning

confidence: 99%

Numerical Quenching for Heat Equations with Coupled Nonlinear Boundary Flux

Edja

Koffi

Koua

et al. 2019

ijaa

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show abstract

“…T h is called the semidiscrete quenching time of (1.4)-(1.7). For study on numerical approximations of heat equation with non-linear boundary conditions we refer to [1,5,[10][11][12][13]16]. Nabongo et al in [12] were interested in the numerical study using a semidiscrete form of…”

Section: Introductionmentioning

confidence: 99%

Numerical quenching of a heat equation with nonlinear boundary conditions

Edja¹,

Touré²,

Koua³

2019

J. Nonlinear Sci. Appl.

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In this paper, we study the quenching behavior of semidiscretizations of the heat equation with nonlinear boundary conditions. We obtain some conditions under which the positive solution of the semidiscrete problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time and obtain some results on numerical quenching rate. Finally we give some numerical results to illustrate our analysis.

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Numerical Study of Estimating the Blow-Up Time of Positive Solutions of Semilinear Heat Equations

Cited by 2 publications

References 0 publications

Numerical Quenching for Heat Equations with Coupled Nonlinear Boundary Flux

Numerical Quenching for Heat Equations with Coupled Nonlinear Boundary Flux

Numerical quenching of a heat equation with nonlinear boundary conditions

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