Advances in Differential Equations

On a class of parabolic equations with variable density and absorption

Robert Kersner, Guillermo Reyes, and Alberto Tesei

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We investigate qualitative properties of solutions to the Cauchy problem for the equation $\rho(x)u_t=(u^m)_{xx}-c_0 u^p$, where $m>1$ and $c_0, p >0$; the initial data are nonnegative with compact support and the density $\rho(x)>0$ satisfies suitable decay conditions as $|x|\to\infty$. If $p \ge m$ and $\rho(x)$ decays not faster than $|x|^{-k}$, where $0 <k \le k^*:=2(p-1)/(p-m)$, the interfaces exist globally in time. On the contrary, if $\rho(x)$ decays faster than $|x|^{-k}$ with $k>k^*$, the interfaces can disappear in finite time. It is also proved that solutions go to zero uniformly as $t \to\infty $, at variance from the case $c_0=0$.

Article information

Adv. Differential Equations Volume 7, Number 2 (2002), 155-176.

First available in Project Euclid: 27 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K65: Degenerate parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35K55: Nonlinear parabolic equations


Kersner, Robert; Reyes, Guillermo; Tesei, Alberto. On a class of parabolic equations with variable density and absorption. Adv. Differential Equations 7 (2002), no. 2, 155--176.

Export citation