Homogenization of ordinary and linear transport equations (Q1907733)

In the framework of homogenization theory the author studies the asymptotic behavior of first-order ordinary differential equations in \(\mathbb{R}^N\) and deals with the associated linear transport equations. The equivalence between G-convergence and strong G-convergence for the ordinary equations is proved. A sufficient condition, which is also necessary in the autonomous case, is given for the weak homogenization of the linear transport equations. This condition is satisfied when \(\text{div } f= 0\).