| Abstract: |
| We consider a semilinear integro-differential equation that arises when introducing inertial effects in the Kuramoto model. Based on the known theory of degenerate Kolmogorov operators, existence, uniqueness and regularity results for the relevant Cauchy problem are discussed. Moreover, a stable numerical operator, which is consistent with the degenerate Kolmogorov operator, is provided in order to produce numerical solutions. Numerical experiments show how the synchronization phenomena depend on the parameters of the Kuramoto model with inertia. |
|