The problem is solved by matching two asymptotic expansions, one solving the initial value problem in a small neighborhood of the initial point, while another one solves the equation at large ...

We study the initial boundary value problem of semilinear hyperbolic equations utt – Δu = f (u) and semilinear parabolic equations ut – Δu = f (u) with critical initial data E (0) = d (or J (u₀) = d), ...