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1 TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

1 2019

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Matrix Green's function of double-diffusivity problem and its applications to problems with inner point source

Chaplya Yevhen, Chernukha Olha, Bilushchak Yurii

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2019

Vol. 23, No 1

75--99

The matrix Green’s function of the initial-boundary value problem of admixture double-diffusivity is defined. The initial-boundary value problem with a point source is formulated for the matrix elements for determination of the matrix Green’s function. Formulae for matrix elements are obtained and the behavior of Green’s functions is investigated. It is shown that the surface generated by the Green’s function has a typical sharp peak in the vicinity of the point of action of the point mass source, and in the vicinity of the top boundary of the layer ,the values of the second element of the Green’s function are times higher than the values of the first one the state of which is corresponding to the quick migration way. On this basis the solutions of the initial-boundary value problems under the action of the internal point source of mass are found. The cases of the deterministic source as well as stochastic ones under uniformand triangular distributions of the coordinate of the mass source location are considered.