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Note on blow-up of solutions for a porous medium equation with convection and boundary flux

100%
Wang Z., Yin J.
Colloquium Mathematicum
|
2012
|
tom 128
|
nr 2
223-228
EN
De Pablo et al. [Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), 513-530] considered a nonlinear boundary value problem for a porous medium equation with a convection term, and they classified exponents of nonlinearities which lead either to the global-in-time existence of solutions or to a blow-up of solutions. In their analysis they left open the case of a certain critical range of exponents. The purpose of this note is to fill this gap.
2
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Positive solutions for one-dimensional singular p-Laplacian boundary value problems

81%
Song H., Yin J., Huang R.
Annales Polonici Mathematici
|
2012
|
tom 105
|
nr 2
125-144
EN
We consider the existence of positive solutions of the equation $1/λ(t) (λ(t)φ_p(x'(t)))' + μf(t,x(t),x'(t)) =0$, where $φ_p(s) = |s|^{p-2}s$, p > 1, subject to some singular Sturm-Liouville boundary conditions. Using the Krasnosel'skiĭ fixed point theorem for operators on cones, we prove the existence of positive solutions under some structure conditions.
3
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Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations

81%
Li J., Yin J., Jin C.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1435-1447
EN
This paper is mainly concerned with the blow-up and global existence profile for the Cauchy problem of a class of fully nonlinear degenerate parabolic equations with reaction sources.
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