  Due to the importance of understanding the formation of the nonlinear
structures in the universe and stellar systems, the nonlinear Jeans instability
which plays the key role in these formation problems is a long-standing open
problem presented by astrophysics more than one hundred years. In this article,
we focus on a reduced model of the nonlinear Jeans instability for the
expanding Newtonian universe which is characterized by a class of second order
nonlinear hyperbolic equations
  \begin{equation*}
  \Box \varrho(x^\mu) +\frac{\mathcal{a} }{t} \partial_{t}\varrho(x^\mu) -
  \frac{\mathcal{b}}{t^2} \varrho(x^\mu) (1+ \varrho(x^\mu) )
-\frac{\mathcal{c}-\mathcal{k}}{1+\varrho(x^\mu)}
(\partial_{t}\varrho(x^\mu))^2= \mathcal{k} F(t).
  \end{equation*} We establish a family of nonlinear self-increase blowup
solution (the solution itself becomes infinite, stable ODE-type blowup) to this
equation and give estimates on the growth rate of $\varrho$ which may explain
the much faster growth rate of the nonlinear structures of universe in
astrophysical observations than the rate given by the classical Jeans
instability.
