Quenching time for a system of semilinear heat equations

Boni, Théodore K.; Nachid, Halima; Nabongo, Diabate

doi:10.18514/mmn.2010.191

Cited by 1 publication

(1 citation statement)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nonlinear parabolic systems like (1.1)-(1.4) come from chemical reactions, heat transfer, etc, where u and v represent the temperatures of two different materials during heat propagation. The quenching phenomenon of parabolic problems has been the issue of intensive study (see for example [3,4,[8][9][10] and the references cited therein), particulary the study of heat equations system with nonlinear boundary conditions has been the subject of investigation of several authors in recent years (see [6,7,14,15,17] and the references cited therein). In [7] the authors study this problem, they prove that the solution (u, v) quenches in finite time T and the quenching occurs only at the boundary x = 0 for 0 < u 0 , v 0 ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

Numerical Quenching for Heat Equations with Coupled Nonlinear Boundary Flux

Edja

Koffi

Koua

et al. 2019

ijaa

View full text Add to dashboard Cite

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.

show abstract