一类带非牛顿位势的广义Vlasov方程

his paper is concerned with a class of generalized Vlasov equations which models the transports of particles under the influence of the non-Newtonian potential. Without requiring the hypothesis of cut-off velocity, the existence and uniqueness of global mild solution with and local mild solution with are established by the contraction mapping principle in one dimension. The proof is based on Green function techniques and parabolic regularization. This result generalizes the previous result by Yan[7], which deals with the solution with cut-off velocity.