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 Univ
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this article, we study the blow up behavior of the heat equation u(t) = u(xx) with u(x) (0, t) = u(p) (0,t), u(x) (a,t) = u(q) (a,t). We also study the quenching behavior of the nonlinear parabolic equation v(t) = v(xx) +2v(x)(2) /(1-v) with v(x)(0,t) = (1-v(0, t))(-p+2), v(x)(a,t) = (1-v (a, t)(-q+2). In the blow up problem, if u(0) 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 v(t) 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.
Açıklama
Anahtar Kelimeler
Heat equation, nonlinear parabolic equation, blow up, nonlinear boundary condition, quenching, maximum principle
Kaynak
Electronic Journal of Differential Equations
WoS Q Değeri
Q2
