Blow-up of solutions of semilinear Euler-Poisson-Darboux equations with nonlocal boundary conditions

摘要

This article studies the hyperbolic initial nonlocal boundary-value problem, utt + (k/t)ut −uxx = ƒ(u), 0 < x < a, t > 0, u(x,0) = u0(x), ut(x,0) = 0, 0 < x < a, u(0, t) = ƒ00M(y) ¦ u(y, t) ¦pdy, t > 0, u(a,t) = ƒ0aN(y) ¦ u(y, t) ¦q dy, t > 0, where k is a real number, p and q are nonnegative constants, and ƒ, u0, M and N are given functions. Criteria for u to blow up in finite time are given.