On the finite time blow-up for filtration problems with nonlinear reaction

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 te...

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Bibliographic Details
Published inApplied mathematics letters Vol. 42; pp. 47 - 52
Main Authors Fellner, K., Latos, E., Pisante, G.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2015
Subjects
Diffusion
Filtration
Filtration problem
Finite time blow-up
Mathematical analysis
Maximal solutions
Nonlinear diffusion
Nonlinearity
Reaction diffusion problems
Robin boundary conditions
Filtration problem
Maximal solutions
Robin boundary conditions
Reaction diffusion problems
Nonlinear diffusion
Finite time blow-up
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Summary: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.
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content type line 23
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2014.11.006