## Advances in Differential Equations

- Adv. Differential Equations
- Volume 7, Number 1 (2002), 77-97.

### Dynamics of solutions of a singular diffusion equation

#### Abstract

In this paper we will obtain the asymptotic profile of solutions of the equation $u_t=\Delta$ log $u$, $u>0$, in $\Omega\times (0,\infty)$, $u=c_1$ on $\partial\Omega\times (0,\infty)$, $u(x,0)=u_0(x)\ge 0$ on $\Omega\subset R^n$ for all $n\in\mathcal {Z}^+$ and $0 <c_1 <\infty$ where $\Omega$ is a smooth, convex, bounded domain.

#### Article information

**Source**

Adv. Differential Equations Volume 7, Number 1 (2002), 77-97.

**Dates**

First available in Project Euclid: 27 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1356651876

**Mathematical Reviews number (MathSciNet)**

MR1867705

**Zentralblatt MATH identifier**

1027.35055

**Subjects**

Primary: 35K57: Reaction-diffusion equations

Secondary: 35B40: Asymptotic behavior of solutions 35K65: Degenerate parabolic equations

#### Citation

Hsu, Shu-Yu. Dynamics of solutions of a singular diffusion equation. Adv. Differential Equations 7 (2002), no. 1, 77--97. https://projecteuclid.org/euclid.ade/1356651876