Thermal blow-up in a subdiffusive medium due to a nonlinear boundary flux
2014 ◽
Vol 17
(1)
◽
Keyword(s):
Blow Up
◽
AbstractA fractional heat equation is used to model thermal diffusion in a one-dimensional bar that exhibits subdiffusive behavior. The left end of the bar is subjected to a nonlinear influx of heat. For the boundary constraint at the right end of the bar, two cases are considered, namely a homogeneous Neumann condition and a homogeneous Dirichlet condition. By reducing both cases to a nonlinear Volterra equation, it is shown that a blow-up always occurs. The asymptotic behavior near the blow-up is determined for both cases. It is also shown that the solution for the Neumann case dominates that of the Dirichlet case.
2014 ◽
Vol 2014
(1)
◽
pp. 234
2012 ◽
Vol 86
(3)
◽
pp. 440-447
2008 ◽
Vol 51
(3)
◽
pp. 785-805
◽
2016 ◽
Vol 40
(1)
◽
pp. 115-128
◽
2015 ◽
Vol 66
(5)
◽
pp. 2525-2541
◽
2016 ◽
Vol 32
◽
pp. 338-354
◽