Keywords: linear partial differential equations.
@article{VYURM_2011_5_a4,
author = {V. V. Karachik},
title = {Polynomial solutions to partial differential equations with constant {coefficients~II}},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
pages = {27--38},
year = {2011},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VYURM_2011_5_a4/}
}
TY - JOUR AU - V. V. Karachik TI - Polynomial solutions to partial differential equations with constant coefficients II JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika PY - 2011 SP - 27 EP - 38 IS - 5 UR - http://geodesic.mathdoc.fr/item/VYURM_2011_5_a4/ LA - ru ID - VYURM_2011_5_a4 ER -
%0 Journal Article %A V. V. Karachik %T Polynomial solutions to partial differential equations with constant coefficients II %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika %D 2011 %P 27-38 %N 5 %U http://geodesic.mathdoc.fr/item/VYURM_2011_5_a4/ %G ru %F VYURM_2011_5_a4
V. V. Karachik. Polynomial solutions to partial differential equations with constant coefficients II. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 5 (2011), pp. 27-38. http://geodesic.mathdoc.fr/item/VYURM_2011_5_a4/
[1] Karachik V. V., “Polynomial solutions to partial differential equations with constant coefficients, I”, Vestnik JuUrGU. Serija «Matematika. Mehanika. Fizika», 10(227):4 (2011), 4–17 (in Russ.)
[2] K. Zweiling, Grundlagen einer Theorie der biharmonishen Polynome, Verlag Technik, Berlin, 1952, 128 pp.
[3] Bicadze A. V., Trudy Tbilisskogo universiteta, 84:35–37 (1962) (in Russ.)
[4] E. P. Miles, E. Williams, “Basic sets of polynomials for the iterated Laplace and wave equations”, Duke Math. Journ., 26:1 (1959), 35–40 | DOI
[5] W. Watzlawek, “Wärmpolynome-Modell fur besondere Losungssysteme bei linearen partiellen Differentialgleichungen”, Berichte Math.-Statist. Sekt. Forschungszentrum Graz., 211 (1983), 1–34
[6] G. N. Hile, A. Stanoyevitch, “Polynomial solutions to Cauchy problems for complex Bessel operators”, Complex Variables, 50:7–11 (2005), 547–574 | DOI
[7] Bondarenko B. A., The basic system of polynomial and quasipolynomial solutions of partial differential equations, FAN, Tashkent, 1987, 127 pp. (in Russ.)
[8] Karachik V. V., Dif. uravnenija, 27:3 (1991), 534–535 (in Russ.)
[9] Karachik V. V., Antropova N. A., “On the solution of the inhomogeneous polyharmonic equation and the inhomogeneous Helmholtz equation”, Differential Equations, 46:3 (2010), 387–399 | DOI
[10] V. V. Karachik, “Normalized system of functions with respect to the Laplace operator and its applications”, Journal of Mathematical Analysis and Applications, 287:2 (2003), 577–592 | DOI
[11] Filatov A. N., Generalized Lie series and their applications, AN UzSSR, Tashkent, 1963, 108 pp. (in Russ.)
[12] Bicadze A. V., The equations of mathematical physics, Nauka, M., 1982, 336 pp. (in Russ.)