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Keywords:
dispersion of gas exhalations; atmosphere over a hilly terrain; chemical reaction; boundary value problem; elliptic equation; distribution of exhalations; existence; uniqueness; regularity; very weak solution
dispersion of gas exhalations; atmosphere over a hilly terrain; chemical reaction; boundary value problem; elliptic equation; distribution of exhalations; existence; uniqueness; regularity; very weak solution
Summary:
The process of gas exhalations in the lower layer of the atmosphere and the problem of distribution of new sources of exhalations in a hilly terrain are studied. Among other, the following assumptions are introduced: (1) the terrain is a hilly one, (2) the exhalations enter a chemical reaction with the atmosphere, (3) the process is stationary, (4) the vector of wind velocity satisfies the continuity equation. The mathematical formulation of the problem then is a mixed boundary value problem for an elliptic equation with the given distribution on its righthand side. It is shown that the problem has a unique "very weak" solution which is sufficiently smooth if so are the coefficients of diffusion and the components of the wind velocity vector. Futher, the problem of distribution of new sources of exhalations is discussed and a method of calculation of its solution is suggested.
References:
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