Geodesic
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 
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/
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     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},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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