<p>Understanding the formation of nonlinear structures in the universe and stellar systems is crucial. The nonlinear Jeans instability plays a key role in these formation processes. It has been a long-standing open problem in astrophysics for more than a century. In this article, we focus on a reduced model of the nonlinear Jeans instability in an expanding Newtonian universe, which is described by a class of second-order nonlinear hyperbolic equations. <Equation ID="Equ123"> <MediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3260_Article_Equ123.gif" Format="GIF" Height="43" Rendition="HTML" Resolution="72" Type="Linedraw" Width="516" /> </MediaObject> <EquationSource Format="TEX">\(\begin{aligned} \Box \varrho (x^\mu ) +\frac{\mathcal {a} }{t} {\partial _{t}}\varrho (x^\mu ) - \frac{\mathcal {b}}{t^2} \varrho (x^\mu ) (1+ \varrho (x^\mu ) ) -\frac{\mathcal {c}-\mathcal {k}}{1+\varrho (x^\mu )} ({\partial _{t}}\varrho (x^\mu ))^2= \mathcal {k}F(t). \end{aligned}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <mo>□</mo> <mi>ϱ</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mi>μ</mi> </msup> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mfrac> <mi mathvariant="script">a</mi> <mi>t</mi> </mfrac> <msub> <mi>∂</mi> <mi>t</mi> </msub> <mi>ϱ</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mi>μ</mi> </msup> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <mfrac> <mi mathvariant="script">b</mi> <msup> <mi>t</mi> <mn>2</mn> </msup> </mfrac> <mi>ϱ</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mi>μ</mi> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>ϱ</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mi>μ</mi> </msup> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <mfrac> <mrow> <mi mathvariant="script">c</mi> <mo>-</mo> <mi mathvariant="script">k</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>ϱ</mi> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mi>μ</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mfrac> <msup> <mrow> <mo stretchy="false">(</mo> <msub> <mi>∂</mi> <mi>t</mi> </msub> <mi>ϱ</mi> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mi>μ</mi> </msup> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mi mathvariant="script">k</mi> <mi>F</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation>We establish a family of nonlinear self-increasing blowup solutions (where the solution itself becomes infinite in a stable ODE-type blowup) for this equation. Furthermore, we provide estimates on the growth rate of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3260_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varrho \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϱ</mi> </math></EquationSource> </InlineEquation>, which may help explain why the nonlinear structures in the universe grow much faster in astrophysical observations than predicted by the classical Jeans instability.</p>