Abstract:
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.
Citation:
È. I. Semenov, G. A. Rudykh, “Exact Non-Self-Similar Solutions of the Equation”, Mat. Zametki, 70:5 (2001), 787–792; Math. Notes, 70:5 (2001), 714–719