Mathematics > Probability
[Submitted on 8 Apr 2018 (v1), last revised 21 May 2018 (this version, v3)]
Title:On stiff problems via Dirichlet forms
View PDFAbstract:The stiff problem is concerned with a thermal conduction model with a singular barrier of zero volume. In this paper, we shall build the phase transitions for the stiff problems in one-dimensional space. It turns out that every phase transition definitely depends on the total thermal resistance of the barrier, and the three phases correspond to the so-called impermeable pattern, semi-permeable pattern and permeable pattern of thermal conduction respectively. For each pattern, the related boundary condition of the flux at the barrier is also derived. Mathematically, we shall introduce and explore the so-called snapping out Markov process, which is the probabilistic counterpart of semi-permeable pattern in the stiff problem.
Submission history
From: Liping Li [view email][v1] Sun, 8 Apr 2018 05:44:29 UTC (49 KB)
[v2] Wed, 18 Apr 2018 17:14:55 UTC (51 KB)
[v3] Mon, 21 May 2018 16:18:41 UTC (1,082 KB)
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