## Differential and Integral Equations

### Quenching for a diffusive equation with a concentrated singularity

#### Abstract

The diffusion equation with a concentrated singular reaction $v_t=v_{xx} + \epsilon\delta(x-a)f(v)$ $(\epsilon>0, 0<a<1)$ is studied. Criteria for global existence and finite time quenching of the solution are established. The growth rate and estimate on quenching time are also given for a certain class of nonlinearities.

#### Article information

Source
Differential Integral Equations, Volume 10, Number 2 (1997), 369-379.

Dates
First available in Project Euclid: 2 May 2013

https://projecteuclid.org/euclid.die/1367526343

Mathematical Reviews number (MathSciNet)
MR1424817

Zentralblatt MATH identifier
0891.35061

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

#### Citation

Deng, Keng; Roberts, Catherine A. Quenching for a diffusive equation with a concentrated singularity. Differential Integral Equations 10 (1997), no. 2, 369--379. https://projecteuclid.org/euclid.die/1367526343