Formula_11569

\[\begin{gathered}\frac{\partial F}{\partial t}+v \frac{\partial F}{\partial x}=-\frac{1}{T^{0}}\left(F-G(v) \int_{v_{1}}^{v_{2}} F\left(x, v^{\prime}, t\right) d v^{\prime}\right)+ \\+(1-p) F(x, v, t) \int_{v_{1}}^{v_{2}}\left(v-v^{\prime}\right) F\left(x, v^{\prime}, t\right) d v^{\prime}, \\F(x, v, 0)=f(x, v), \quad x \in[0, L], \quad v \in\left[v_{1}, v_{2}\right], \\F(0, v, t)=h(v, t), \quad t>0, \quad v \in\left[v_{1}, v_{2}\right] .\end{gathered}\]