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Applied Math Seminar
Maxwell Boundary Condition for Boltzmann Equation
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The Boltzmann equation in the kinetic theory offers physically realistic modelling of the boundary condition on the solid. This makes it possible to understand some basic physical phenomena, for which the fluid equations such as the Navier-Stokes and Euler equations cannot. However, there has been little analytical studies of this important aspect. We introduce a stochastic formulation of the boundary condition of Maxwell types. This allows for the application of probabilistic methods in the study of boundary effects. We illustrate this approach by studying problems such as the thermal stress and diffusion in the gravitational field. |