Blow-Up for a Semilinear Parabolic Equation With Nonlinear Memory and Nonlocal Nonlinear Boundary

Blow-up for Discretizations of a Nonlinear Parabolic Equation With Nonlinear Memory and Mixt Boundary Condition

“…Let us notice that in (Abia et al,1998), only the semi-discrete scheme has been analyzed. One may find in (Mai et al, 1991;Brandle et al, 2004;Ferreira et al, 2004;Li and Xie, 2004;Kozhanov, 1994;N'gohisse and Boni, 2011;Pablo and al, 2005), similar studies concerning other parabolic problems. Let us notice that many authors have used numerical methods to study the phenomenon of blow-up but they are only a few studies on the convergence of the numerical blows-up time for solutions which blow-up in L ∞ norm.…”

Blow-up for a degenerate and singular parabolic equation with nonlocal boundary condition

“…They obtained some results on the existence and nonexistence of the global solutions, and derived the uniform blow-up profile estimate under some assumptions. For other works on this topic, we refer the readers to [8,9,10,19,21] and the references therein.…”

Global existence of solutions of initial boundary value problem for nonlocal parabolic equation with nonlocal boundary condition

“…Now suppose that q = 1, min(r, p) ≥ 1 and (47) holds. Multiplying (1) by (x) exp( 1 t), where (x) is defined in (9) and (28), and integrating the obtained equation over Ω, from (27), (29), Green's identity, and Jensen's inequality, we obtain Further, we consider the case q > 1. To prove blow-up of all nontrivial solutions, we need an universal lower bound for solutions of (1)- (3).…”

“…In particular, the blow-up problem for nonlocal parabolic equations with boundary condition (2) was investigated in literature. [25][26][27][28][29][30][31][32] So, for example, Cui et al 25 studied (1)-(3) with b(x, t) ≡ 0, a(x, t) ≡ a(x) and k(x, , t) ≡ k(x, ), and problem (1)-(3) with r = 0, a(x, t) ≡ 1, b(x, t) ≡ b > 0 and k(x, , t) ≡ k(x, ) was considered in Mu et al 30 Gladkov and Guedda 8 studied (1)-(3) with a(x, t) ≡ 0. The existence of classical local solutions and the comparison principle for (1)-(3) were proved in Gladkov and Kavitova.…”