On stiff problems via Dirichlet forms

2018/04/08 by Liping Li, Wenjie Sun, Li, Liping +1
Computer Science · Mathematics · #31C25 #60J25 #60J45 #60J50 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1804.02634

openalex publication_date 2018/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• An open microscopic model of heat conduction: evolution and\n non-equilibrium stationary states
• Explicit solutions for the Solomon-Wilson-Alexiades's mushy zone model with convective or heat flux boundary conditions
• Regularity of solutions to a model for solid-solid phase transitions driven by configurational forces
• A parabolic free transmission problem: flat free boundaries are smooth
• Weak asymptotic solution of the phase field system in the case of confluence of free boundaries in the Stefan problem with undercooling