Exact solutions of the nonlinear diffusion equation $u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 265-278
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Investigating exact solutions of the nonlinear diffusion equation, which arises in wave problems in hydrodynamics and heat transfer processes, we find new classes of solutions of this equation in a two-dimensional coordinate space and demonstrate a special superposition principle that allows constructing complex multimode solutions from the simplest two- and three-mode solutions.
@article{TMF_2000_124_2_a5,
author = {V. M. Zhuravlev},
title = {Exact solutions of the nonlinear diffusion equation $u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {265--278},
publisher = {mathdoc},
volume = {124},
number = {2},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a5/}
}
TY - JOUR AU - V. M. Zhuravlev TI - Exact solutions of the nonlinear diffusion equation $u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2000 SP - 265 EP - 278 VL - 124 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a5/ LA - ru ID - TMF_2000_124_2_a5 ER -
%0 Journal Article %A V. M. Zhuravlev %T Exact solutions of the nonlinear diffusion equation $u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space %J Teoretičeskaâ i matematičeskaâ fizika %D 2000 %P 265-278 %V 124 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a5/ %G ru %F TMF_2000_124_2_a5
V. M. Zhuravlev. Exact solutions of the nonlinear diffusion equation $u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 2, pp. 265-278. http://geodesic.mathdoc.fr/item/TMF_2000_124_2_a5/