Department of Mathematics, University of Rhode Island, Kingston, RI 02881 USA
Abstract:
In this paper, we show that the initial boundary value problem for the (singular) nonlinear EPD (Euler-Poisson-Darboux) equation does not possess global solutions for arbitrary choices of ) when 0 < k ? 1 for a wide class of nonlinearities , which includes all the even powers of u and the functions u2n + 1, n = 1, 2,…. The solutions are assumed to vanish on the “walls” of the spacetime cylinder and satisfy . The result is independent of the space dimension.