Theory of Electromagnetic Research-on Solutions of Nonlinear Wave Equations

摘要

It is shown that for certain nonlinear functions f(u) solutions of the Cauchy problem for the equation become infinite at a finite value of t. The number of space dimensions is one, two or three and the initial data must satisfy appropriate conditions. A similar result is established for the nonlinear Euler-Poisson-Darboux for two space variables and k > 1. The results are based upon a comparison theorem which enables us to compare different solutions of the same or of related equations.