Blow-Up Rate

Abstract

It is established in Chap. 5 that the nonlinearity causes the blow-up to occur at a finite time in certain situations. If the solution to the ODE $u_t \,= \,f(u)$, blows up at a finite time t = T with $u(T - 0) = +\infty$, then u = G(T - t), where $G(\xi)$ is the inverse function of $\int\nolimits_\infty^u \frac {dn}{f(n)}$