On the quenching set for a fast diffusion equation: regional quenching
2005 ◽
Vol 135
(3)
◽
pp. 585-602
Keyword(s):
Blow Up
◽
We study positive solutions of a very fast diffusion equation, ut = (um−1ux)x, m < 0, in a bounded interval, 0 < x < L, with a quenching-type boundary condition at one end, u (0, t) = (T − t)1/(1 − m) and a zero-flux boundary condition at the other, (um −1ux)(L, t) = 0. We prove that for m ≥ −1 regional quenching is not possible: the quenching set is either a single point or the whole interval. Conversely, if m < −1 single-point quenching is impossible, and quenching is either regional or global. For some lengths the above facts depend on the initial data. The results are obtained by studying the corresponding blow-up problem for the variable v = um −1.
2005 ◽
Vol 135
(3)
◽
pp. 585-602
2003 ◽
Vol 33
(1)
◽
pp. 123-146
◽
Keyword(s):
2020 ◽
Vol 482
(1)
◽
pp. 123526
Existence and large time behaviour of finite points blow-up solutions of the fast diffusion equation
2018 ◽
Vol 57
(5)
◽
Keyword(s):
Blow Up
◽