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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

References:

[1] M. E. Berliand: **Present problem of the atmospherical diffusion and the air pollution**. Leningrad (1975) (in Russian).

[2] M. E. Berliand, coll.: **Optimal distribution of the exhalation sources of the air pollution**. Trudy GGO, N. 325, (1975), 3-25.

[3] A. Kufner O. John, S. Fučík: **Function spaces**. Academia, Praha (1973).

[4] M. Hino: **Computer experiment on smoke diffusion over a complicated topography**. J. Atm. Environm 2, (1968) 541-558. DOI 10.1016/0004-6981(68)90063-2

[5] O. A. Ladyzhenskaja: **Boundary value problems of the mathematical physics**. Moscow (1973) (in Russian).

[6] O. A. Ladyzhenskaja, N. N. Urаľсеvа: **Linear and Quasilinear Equations of Elliptic type**. Academic Press, New York (1968).

[7] G. I. Marchuk: **Mathematical modelling in the problem of environment**. Moscow (1982) (in Russian). MR 0681121 | Zbl 0493.90001

[8] J. Nečas: **Les methodes directes en theorie des equations elliptiques**. Praha (1967). MR 0227584

[9] Tran Dien Hien: **The Dirichlet problem in the dispersion of gas exhalations over a wet hilly surface**. CMUC 4 (12). (1984), 459-471. MR 0775564 | Zbl 0558.35024

[10] O. G. Sutton: **Micrometeorology**. Mc Graw Hill, London (1952).

[11] J. Stará M. Tenčlová J. Bubník S. Fučík O. John: **Gas exhalation and its calculation. (Part 1)**. Apl. mat. 26 (1981), 30-44. MR 0602400