我们研究了具有多重碎片的空间非均匀凝聚凝聚过程，证明了与凝聚核对应的模型方程的连续解的存在性

$$\mathrm{<trans\; data-src="K">K（K）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="y">年</trans>}<trans\; data-src=")">)</trans><trans\; data-src="\le ">\le </trans>{\mathrm{<trans\; data-src="k">k</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="k">k</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="(">(</trans>{\mathrm{<trans\; data-src="x">x个</trans>}}^{\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}}<trans\; data-src="+">+</trans>{\mathrm{<trans\; data-src="y">年</trans>}}^{\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}}<trans\; data-src=")">)</trans><trans\; data-src=" "> </trans>\text{<trans data-src="for">对于</trans>}<trans\; data-src=" "> </trans>\mathrm{<trans\; data-src="x">x个</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="y">年</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="\infty ">\infty </trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans><trans\; data-src=" "> </trans>\text{<trans data-src="where">哪里</trans>}<trans\; data-src=" "> </trans>\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src="]">]</trans><trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="k">k</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}<trans\; data-src=",">,</trans>{\mathrm{<trans\; data-src="k">k</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">,</trans>$$

至少有一个${\mathrm{<trans\; data-src="k">k</trans>}}_{\mathrm{<trans\; data-src="0">0</trans>}}$和${\mathrm{<trans\; data-src="k">k</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}$非零。这种形式的凝聚核包括几个实用核。该研究包括模型方程中的碎片部分，并考虑了多个碎片核。最后，还研究了解的唯一性。