Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 131, pp. 1-14.
Title: Quenching for singular and degenerate quasilinear diffusion equations
Authors: Yuanyuan Nie (Jilin Univ., Changchun, China)
Chunpeng Wang (Jilin Univ., Changchun, China)
Qian Zhou (Jilin Univ., Changchun, China)
Abstract:
This article concerns the quenching phenomenon of the solution to
the Dirichlet problem of a singular and degenerate quasilinear diffusion
equation. It is shown that there exists a critical length for the special
domain in the sense that the solution exists globally in time if
the length of the special domain is less than this number while the
solution quenches if the length is greater than this number.
Furthermore, we also study the quenching properties for the quenching solution,
including the location of the quenching points and the blowing up of the
derivative of the solution with respect to the time at the quenching time.
Submitted January 23, 2013. Published May 29, 2013.
Math Subject Classifications: 35K65, 35K67, 35B40.
Key Words: Quench; singular; degenerate.