Abstract
This paper deals with blow-up properties of solutions to a nonlocal parabolic system with nonlocal boundary conditions. The global existence and finite time blow-up criteria are obtained. Moreover, for some special cases, we establish the precise blow-up rate estimates.
Highlights
1 Introduction In this article, we consider the positive solution of the following parabolic equations with nonlocal boundary conditions:
Zhong and Tian Boundary Value Problems (2015) 2015:61 which is subjected to homogeneous Dirichlet boundary condition. They proved that there exists no global positive solution if ∞ /(sf (s)) ds < ∞ and φ(x) dx > /a, where φ is the unique positive solution of the linear elliptic problem
The main results of this paper are the following theorems
Summary
We consider the positive solution of the following parabolic equations with nonlocal boundary conditions:. Deng et al [ ] studied the parabolic equation with nonlocal source ut = f (u) u + a u dx , x ∈ , t > , Zhong and Tian Boundary Value Problems (2015) 2015:61 which is subjected to homogeneous Dirichlet boundary condition. They proved that there exists no global positive solution if ∞ /(sf (s)) ds < ∞ and φ(x) dx > /a, where φ is the unique positive solution of the linear elliptic problem. The main results of this paper are the following theorems
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