Abstract
This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an infinitely long cylinder. We study the effects of the strength of the source on quenching. Criteria for global existence of the solution and for quenching are investigated.
Highlights
License (CC BY 4.0).http://creativecommons.org/licenses/by/4.0/ The quenching phenomena have been studied since 1975 [1]
The model involves a concentrated source, such as in a chemical reaction process due to the effect of a catalyst, or in the ignition of a combustible medium through the use of either a heated wire or a pair of small electrodes to supply a large amount of energy to a very confined area [2]
We study the quenching problem with a concentrated nonlinear source in the unbounded domain, the infinitely long cylinder
Summary
In 2006, the quenching problem with a concentrated source has been posted correctly in a multi-dimensional bounded domain by Chan [3]. We study the quenching problem with a concentrated nonlinear source in the unbounded domain, the infinitely long cylinder. We let Ω and ω be the infinitely long cylinders centered at the origin with the radii R and b respectively. We study the following problem in the infinitely long cylinder Ω with a concentrated nonlinear source on ∂ω:. Since D is bounded, let us state the results by Chan [3] in the following theorem.
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