Bondarenko, B. A.; Pirniyazova, P. M. Normalized systems of functions and their applications to the solution of problems of diffusion equations. (Russian. English summary) Zbl 1211.35065 Vopr. Vychisl. Prikl. Mat. 119, 39-49, 135 (2008). Summary: Based on normalized systems of functions with respect to differential operators, the basic sets of polynomial and quasipolynomial solutions of the diffusion equations are constructed and investigated. These solutions are used for solving Cauchy problems. MSC: 35C05 Solutions to PDEs in closed form 35K15 Initial value problems for second-order parabolic equations Keywords:polynomial and quasipolynomial solutions PDFBibTeX XMLCite \textit{B. A. Bondarenko} and \textit{P. M. Pirniyazova}, Vopr. Vychisl. Prikl. Mat. 119, 39--49, 135 (2008; Zbl 1211.35065)