Quenching behavior of semilinear heat equations with singular 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 quenching behavior of solution to the semilinear heat equation (Formula presented) with f(v) = u-r or (1 – v)–r and (Formula presented) For this, we utilize the quenching problem ut=uxx with ux(0,t)=u-p(0,t), ux(a,t)=(1-u(a,t))-q. In the second problem, if u0 is an upper solution (a lower solution) then we show that quenching occurs in a finite time, the only quenching point is x=0 (x=a) and utblows up at quenching time. Further, we obtain a local solution by using positive steady state. In the first problem, we first obtain a local solution by using monotone iterations. Finally, for f(v)=-v-r ((1-v)-r), if v0 is an upper solution (a lower solution) then we show that quenching occurs in a finite time, the only quenching point is x=0 (x=a) and vt blows up at quenching time. © 2015 Texas State University.
Açıklama
Anahtar Kelimeler
Heat equation, Maximum principle, Monotone iteration, Quenching, Singular boundary condition
Kaynak
Electronic Journal of Differential Equations
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
2015
