Mathematics and Statistics Vol. 2(1), pp. 48 - 53
DOI: 10.13189/ms.2014.020107
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Quenching Behavior of Parabolic Problems with Localized Reaction Term

Chien-Wei Chang , Yen-Huang Hsu , H. T. Liu ^*
Department of Applied Mathematics, Tatung University, Taipei, 10452, Taiwan

ABSTRACT

Let p, q, T be positive real numbers, B = {x ∈ Rⁿ : }, ∂B = {x ∈ Rⁿ : }, x^∗ ∈ B, △ be the Laplace operator in Rⁿ. In this paper, the following the initial boundary value problem with localized reaction term is studied: , where u₀ ≥ 0. The existence of the unique classical solution is established. When x^∗ = 0, quenching criteria is given. Moreover, the rate of change of the solution at the quenching point near the quenching time is studied.

KEYWORDS
Finite time quenching, quenching rate, localized reaction

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Chien-Wei Chang , Yen-Huang Hsu , H. T. Liu , "Quenching Behavior of Parabolic Problems with Localized Reaction Term," Mathematics and Statistics, Vol. 2, No. 1, pp. 48 - 53, 2014. DOI: 10.13189/ms.2014.020107.

(b). APA Format:
Chien-Wei Chang , Yen-Huang Hsu , H. T. Liu (2014). Quenching Behavior of Parabolic Problems with Localized Reaction Term. Mathematics and Statistics, 2(1), 48 - 53. DOI: 10.13189/ms.2014.020107.