Blow up and quenching for a problem with nonlinear boundary conditions
Küçük Resim Yok
Tarih
2015
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Texas State University - San Marcos
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this article, we study the blow up behavior of the heat equation ut = uxx with ux(0, t) = up(0, t), up(0, t) = ux(a, t). We also study the quenching behavior of the nonlinear parabolic equation vt = vxx +2v2x =(1-v) with vx(0, t) = (1 - v(0, t))-p+2, vx(a, t) = (1 v(a; t))-q+2. In the blow up problem, if u0 is a lower solution then we get the blow up occurs in a finite time at the boundary x = a and using positive steady state we give criteria for blow up and non-blow up. In the quenching problem, we show that the only quenching point is x = a and vt blows up at the quenching time, under certain conditions and using positive steady state we give criteria for quenching and non-quenching. These analysis is based on the equivalence between the blow up and the quenching for these two equations. © 2015 Texas State University - San Marcos.
Açıklama
Anahtar Kelimeler
Blow up, Heat equation, Maximum principle, Nonlinear boundary condition, Nonlinear parabolic equation, Quenching
Kaynak
Electronic Journal of Differential Equations
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
2015
