Quenching for Porous Medium Equations

Küçük Resim Yok

Tarih

2022

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

Künye