Geodesic
Exact Non-Self-Similar Solutions of the Equation
Matematičeskie zametki, Tome 70 (2001) no. 5, pp. 787-792

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In this paper, we obtain new exact non-self-similar solutions of the nonlinear diffusion equation $$ u_t=\Delta \ln u,\quad u\triangleq u(\mathbf x,t):\Omega\times\mathbb R^+\to\mathbb R, \quad\mathbf x\in\mathbb R^n, $$ where $\Omega\subset\mathbb R^n$ is the domain and $\mathbb R^+=\{t:0\le t+\infty\}$, $u(\mathbf x,t)\ge0$ is the temperature of the medium. 
@article{MZM_2001_70_5_a13,
     author = {\`E. I. Semenov and G. A. Rudykh},
     title = {Exact {Non-Self-Similar} {Solutions} of the {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {787--792},
     publisher = {mathdoc},
     volume = {70},
     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a13/}
}
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È. I. Semenov; G. A. Rudykh. Exact Non-Self-Similar Solutions of the Equation. Matematičeskie zametki, Tome 70 (2001) no. 5, pp. 787-792. http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a13/