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

This article studies the hyperbolic initial nonlocal boundary-value problem, u"t"t + (k/t)u"t -u"x"x = @?(u), 0 0, u(x,0) = u"0(x), u"t(x,0) = 0, 0 0, u(a,t) = @?"0^aN(y) | u(y, t) |^q dy, t > 0, where k is a real number, p and q are nonnegative constants, and @?, u"0, M and N are given functions. Criteria for u to blow up in finite time are given.