论文标题
碰撞引起的断裂方程的存在和不存在
Existence and non-existence for the collision-induced breakage equation
论文作者
论文摘要
考虑了用于碰撞引起的断裂的数学模型。假设$ k（x，x，y）= x，x，y）= x^y^y^y^y^β + x^βy^βy^y^y le pullinear collision诱导的断裂方程的存在显示，则显示了一大批无限的碰撞核和女儿分布功能，假设$ k（x，x，y）= x，y）= x^y y^y^y^y^y^y^β + x^βy^y^y^y l liw le abe le 1 $ 1 $ 1 $ 1 $ 1 $ 1 $。当[1,2] $中的$α+β\ $α+β\时，始终存在至少一个弱质量稳定的解决方案。相比之下，当$α+β\在[0,1）$和$α\ ge 0 $中时，不存在全球质量质量的弱解决方案，尽管这些解决方案是根据初始条件在有限的时间间隔内构建的。还考虑了独特性问题。最后，对于$α<0 $和特定的女儿分布函数，还建立了质量持续解决方案的不存在。
A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large class of unbounded collision kernels and daughter distribution functions, assuming the collision kernel $K$ to be given by $K(x,y)= x^α y^β + x^β y^α$ with $α\le β\le 1$. When $α+ β\in [1,2]$, it is shown that there exists at least one weak mass-conserving solution for all times. In contrast, when $α+ β\in [0,1)$ and $α\ge 0$, global mass-conserving weak solutions do not exist, though such solutions are constructed on a finite time interval depending on the initial condition. The question of uniqueness is also considered. Finally, for $α<0$ and a specific daughter distribution function, the non-existence of mass-conserving solutions is also established.
