QUENCHING PROBLEMS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM WITH SINGULAR BOUNDARY OUTFLUX
Küçük Resim Yok
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Tamkang Univ
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this paper, we study two quenching problems for the following semilinear reaction-diffusion system: u(t) = u(xx) +(1-v)(-p1), 0 < x < 1, 0 < t < T, v(t) = v(xx) +(1-u)-(p2), 0 < x < 1, 0 < t < T, u(x) (0, t) = 0, u(x) (1, t) = -v (-q1) (1, t), 0 < t < T, v(x) (0, t) = 0, v(x) (1, t) = -u -(q2) (1, t), 0 < t < T, u (x,0) = u(0) (x) < 1, v (x, 0) = v(0) (x) < 1, 0 <= x <= 1, where p(1), p(2), q(1), q(2) are positive constants and u(0)(x), v(0)(x) are positive smooth functions. We firstly get a local exisence result for this system. In the first problem, we show that quenching occurs in finite time, the only quenching point is x = 0 and (u(t), v(t)) blows up at the quenching time under the certain conditions. In the second problem, we show that quenching occurs in finite time, the only quenching point is x = 1 and (u(t), v(t)) blows up at the quenching time under the certain conditions.
Açıklama
Anahtar Kelimeler
Reaction-diffusion system, singular boundary outflux, quenching, maximum principles, monotone iterations
Kaynak
Tamkang Journal of Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
47
Sayı
3
