The continuous dependence of the Rotenberg equation’s solution on the parameters of non-smooth boundary

This paper investigates the Rotenberg equation with non-smooth boundary conditions in L¹ space. We prove that the main operator of the equation is densely defined and resolvent-positive. Furthermore, it is shown that the positive cone in the domain of its adjoint operator is cofinal within the positive cone of the entire adjoint space. Consequently, the spectral bound of the semigroup generated by the main operator is demonstrated to coincide with its growth order. Additionally, the continuous dependence of solutions on boundary parameters is rigorously established.