On the finite time blow-up for filtration problems with nonlinear reaction. (April 2015)

• Record Type: Journal Article
• Authors: Fellner, K.; Latos, E.; Pisante, G.
• Is Part Of: Applied mathematics letters. Volume 42(2015:Apr.)
• Page Start: 47
• Page End: 52
• Publication Date: 2015-04
• Subjects: Finite time blow-up -- Filtration problem -- Nonlinear diffusion -- Robin boundary conditions -- Reaction diffusion problems -- Maximal solutions; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2014.11.006
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow-up of solutions subject to sufficiently large initial data provided that the reaction term "overpowers" the nonlinear diffusion in a certain sense. Secondly, under related assumptions on the nonlinearities, we show that initial data above positive stationary state solutions will always lead to finite time blow-up.