(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 2001)
We study the global existence, long-time behaviour and blow-up of classical solutions of the equation u = u ln^q(1 + u^2) in (3 + 1)-space-time with arbitrary big initial data. Thus we have a case of a repellent potential energy term in the relevant energetic identity, contrary to the attractive energy case described by the well-known equation u = - u|u|^p-1. The global existence result for 0 < q ≤ 2 is first established. Then special "counterdecay" (for 0 < q < 2) and blow-up effects (for q > 2) are found, which show that q = 2 is a "critical" value. In this way it is answered, in particular, to a question that has arisen already in the pioneering works of Keller and Jorgens on the semilinear wave equation.