Regularity, asymptotic behavior and partial uniqueness for Smoluchowski's coagulation equation

Stéphane Mischler, José Alfredo Cañizo

We consider Smoluchowski's equation with a homogeneous kernel of the form $a(x,y)=x^{\alpha }{y}^{\beta }+x^{\beta }{y}^{\alpha }$ with $-1<\alpha \le \beta <1$ and $\lambda :=\alpha +\beta \in (-1,1)$. We first show that self-simila…