Blow up for porous medium equations
Küçük Resim Yok
Tarih
2021
Yazarlar
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Dergi ISSN
Cilt Başlığı
Yayıncı
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In various branches of applied sciences, porous medium equations exist where this basic model occurs in a natural fashion. It has been used to model fluid flow, chemical reactions, diffusion or heat transfer, population dynamics, etc.. Nonlinear diffusion equations involving the porous medium equations have also been extensively studied. However, there has not been much research effort in the parabolic problem for porous medium equations with two nonlinear boundary sources in the literature. This paper adresses the following porous medium equations with nonlinear boundary conditions. Firstly, we obtain finite time blow up on the boundary by using the maximum principle and blow up criteria and existence criteria by using steady state of the equation $k_{t}=k_{xx}^{n},(x,t)\\in (0,L)\\times (0,T)\\ $with $ k_{x}^{n}(0,t)=k^{\\alpha }(0,t)$, $k_{x}^{n}(L,t)=k^{\\beta }(L,t)$,$\\ t\\in (0,T)\\ $and initial function $k\\left( x,0\\right) =k_{0}\\left( x\\right) $,$\\ x\\in \\lbrack 0,L]\\ $where $n>1$, $\\alpha \\ $and $\\beta \\ $and positive constants.
Açıklama
Anahtar Kelimeler
Kaynak
Mathematical Sciences and Applications E-Notes
WoS Q Değeri
Scopus Q Değeri
Cilt
9
Sayı
1
