Quenching for Porous Medium Equations
Küçük Resim Yok
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Tamkang Univ
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
This paper studies the following two porous medium equations with singular boundary conditions. First, we obtain that finite time quenching on the boundary, as well as k(t) blows up at the same finite time and lower bound estimates of the quenching time of the equation k(t) = (k(n))(xx) + (1 - k)(-alpha), (x, t) is an element of (0, L) x (0, T) with (k(n))(x) (0, t) = 0, (k(n))(x) (L, t) = (1 - k(L, t))(-beta), t is an element of (0, T) and initial function k (x, 0) = k(0) (x), x is an element of[0, L] where n > 1, alpha and beta are positive constants. Second, we obtain that finite time quenching on the boundary, as well as k(t) blows up at the same finite time and a local existence result by the help of steady state of the equation k(t) = (k(n))(xx), (x, t) is an element of (0, L) x (0, T) with (k(n))(x) (0, t) = (1 - k(0, t))(-alpha), (k(n))(x) (L, t) = (1 - k(L, t))(-beta), t is an element of(0, T) and initial function k (x, 0) = k(0) (x), x is an element of [0, L] where n > 1, alpha and beta are positive constants.
Açıklama
Anahtar Kelimeler
Maximum principles, Nonlinear diffusion equation, Heat equation, Quenching, Singular boundary condition
Kaynak
Tamkang Journal of Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
53
Sayı
2
