ON NONLOCAL RECURSION OPERATOR AND POLYNOMIAL SOLUTIONS BASIS FOR EQUATION OF UNIFORM LIQUID FILTRATION IN A SEAMYPOROUS MEDIUM
V.E. Shemarulin VANT. Ser.: Mat. Mod. Fiz. Proc 2000. Вып.4. С. 5357.
An integrodifferential recursion operator has been determined for a onedimensional linear uniform equation, describing the process of uniform liquid filtration in seamyporous 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 integrodifferential 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 evolutiontype equations with constant coefficients, as well as for some manydimensional equations, in particular, for two and threedimensional equations of diffusion and filtration.
