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The evolution of dust emitted by a uniform source above ground level. (English) Zbl 1028.35039
Summary: A uniform source situated at a fixed location starts to emit dust at a certain time, $$t=0$$, and maintains the same action for $$t>0$$. The subsequent spread of the dust into space is governed by an initial boundary value problem of the atmospheric diffusion equation. The equation has been solved when the wind speed is uniform and diffusion is present both along the vertical and the horizontal for a general source. The solution is obtained in a closed form. The behaviour of the solution is illustrated by means of two examples, one of which is relevant to industrial pollution and the other to the environment. The solution is represented in graphic form. It is found that the spread of dust into space depends mainly on the type of source and on the horizontal component of diffusion. For weak diffusion, the dust travels horizontally with a vertical front at the uniform speed of the flow. In the presence of horizontal diffusion, dust diffuses vertically and horizontally. For a point source, the distribution of dust possesses a line of extensive pollution. For a finite-line source, the dust concentration possesses a point of accumulation that moves both horizontally and vertically with time.
##### MSC:
 35C15 Integral representations of solutions to PDEs 35Q35 PDEs in connection with fluid mechanics 49K20 Optimality conditions for problems involving partial differential equations
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