Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation

Initial - Boundary Value Problems for Parabolic Equations

A note on critical point and blow-up rates for singular and degenerate parabolic equations

In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

Liouville Theorems, a Priori Estimates, and Blow-up Rates for Solutions of Indefinite Superlinear Parabolic Problems

In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.

Initial Blow-up of Solutions of Semilinear Parabolic Inequalities

We study classical nonnegative solutions u(x, t) of the semilinear parabolic inequalities 0 ≤ ut −∆u ≤ u in Ω× (0, 1) where p is a positive constant and Ω is a bounded domain in R, n ≥ 1. We show that a necessary and sufficient condition on p for such solutions u to satisfy a pointwise a priori bound on compact subsets K of Ω as t→ 0 is p ≤ 1 + 2/n and in this case the bound on u is max x∈K u(x...

Blow-up of solution of an initial boundary value problem for a generalized Camassa-Holm equation

In this paper, we study the following initial boundary value problem for a generalized Camassa-Holm equation