Single-point blow-up for a degenerate parabolic problem with a nonlinear source of local and nonlocal features

摘要

Let q, m and T be any real numbers such that q⩾0, m>1, and T>0. This article studies the following degenerate semilinear parabolic first initial-boundary value problem:xqut(x,t)−uxx(x,t)=amq+2δ(x−b)f(u(x,t))Um(t)for00, and ψ is nontrivial, nonnegative and continuous such that ψ(0)=0=ψ(1), and ψ′′+amq+2δ(x−b)f(ψ(x))Um(0)⩾0 for 0