Vm. Zhuravlev, Exact solutions of the nonlinear diffusion equation u(t) = Delta log u plus lambda u in a two-dimensional coordinate space, THEOR MATH, 124(2), 2000, pp. 1082-1093
Investigating exact solutions of the nonlinear diffusion equation, which ar
ises in wave problems in hydro-dynamics and heat transfer processes, we fin
d new classes of solutions of this equation in a, two-dimensional coordinat
e space and demonstrate a special superposition principle that allows const
ructing complex multimode solutions from the simplest two- and three-mode s
olutions.