I am struggling with the following PDE's stability, my intuitive is to use the semigroup theory, but it seems that I can not even compute the eigenvalues, any other idea?
$$w_t=-aw-b^2\int_o^{2\pi}sin\theta B(t,\theta)d\theta \\ B_t=-w^*B_{\theta}-B^*_\theta w+\lambda B$$
Here a,b are constant and w is a function of t, B is a function of t and $\theta$, $w^*$ and $B^*_\theta$ are known functions.