2022/11/12 by Franco Flandoli, Flandoli, Franco, Ruojun Huang +3 · 1 citation
Mathematics · Medicine · #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Differential Equations and Numerical Methods
paper · pdf · doi:10.48550/arxiv.2211.06693
In the present article we introduce a variant of Smoluchowski's coagulation equation with both position and velocity variables taking a kinetic viewpoint arising as the scaling limit of a system of second-order (microscopic) coagulating particles. We focus on the rigorous study of the PDE system in the spatially-homogeneous case proving existence and uniqueness under different initial conditions in suitable weighted space, investigating also the regularity of such solutions.