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ON NONLOCAL RECURSION OPERATOR AND POLYNOMIAL SOLUTIONS BASIS FOR EQUATION OF UNIFORM LIQUID FILTRATION IN A SEAMY-POROUS MEDIUM

V.E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc 2000. Вып.4. С. 53-57.

An integro-differential recursion operator has been determined for a one-dimensional linear uniform equation, describing the process of uniform liquid filtration in seamy-porous medium (filtration equations). It is shown how a basis can be constructed in the P space of the equation polynomial solutions using this operator. A matrix method for constructing exact solutions is proposed. With this method explicit formulae for polynomials, forming one of the possible P space bases have been gained.
    An integro-differential recursion operator can be used for constructing new exact solutions of a filtration equation, different from polynomial ones, and analytical solutions estimated - for testing numerical techniques and programs intended for computing filtration processes. The matrix method proposed in the paper can be used for constructing exact solutions of a wide range of evolution-type equations with constant coefficients, as well as for some many-dimensional equations, in particular, for two- and three-dimensional equations of diffusion and filtration.










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