We are concerned with a forest kinetic model equipped with the Dirichlet boundary conditions which has been presented by Kuzunetsov et al. (4). We construct global solutions and construct a dynamical system determined from the Cauchy prob- lem of the model equations. It is also shown that the dynamical system possesses a bounded absorbing set and every trajectory has a nonempty ω-limit set in a suitable weak topology. These results are then a modification of those obtained in our previous paper (1) from the Neumann condition case to the Dirichlet condition case. 1 Introduction This paper together with the forth coming two papers are going to be devoted to rewriting our previous results (1, 2, 3) to the case of the Dirichlet boundary conditions. In the papers (1, 2, 3), we have studied a prototype forest kinematic model which was presented by Kuznetsov, Antonovsky, Biktashev and Aponina (4): ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ∂u ∂t = βδw − γ(v)u − fu in Ω × (0, ∞), ∂v ∂t = fu − hv in Ω × (0, ∞), ∂w ∂t = d∆w − βw + αv in Ω × (0, ∞), ∂w ∂n =0 on ∂Ω × (0, ∞), u(x, 0) = u0(x) ,v (x, 0) = v0(x) ,w (x, 0) = w0(x )i n Ω.