Abstract
This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and global existence conditions are obtained. For some special case, we also give out the blow-up rate estimate.
Highlights
In this article, we consider the positive solution of the following degenerate parabolic equation ut = f (u)( u + a u(x, t)dx), x ∈, t > 0, u(x, t) = g(x, y)ul(y, t)dy, x ∈ ∂, t > 0, (1:1)
There have been many articles dealing with properties of solutions to degenerate parabolic equations with homogeneous Dirichlet boundary condition
Deng et al [5] studied the parabolic equation with nonlocal source ut = f (u)( u + a udx), (1:2)
Summary
1. Introduction In this article, we consider the positive solution of the following degenerate parabolic equation ut = f (u)( u + a u(x, t)dx), x ∈ , t > 0, u(x, t) = g(x, y)ul(y, t)dy, x ∈ ∂ , t > 0, (1:1) Chen and Liu [14] considered the following nonlinear parabolic equation with a localized reaction source and a weighted nonlocal boundary condition ut = f (u)( u + au(x0, t)) , x ∈ , t > 0, u(x, t) = g(x, y)u(y, t)dy, x ∈ ∂ , t > 0, (1:6)
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