Existence and Uniqueness of the Mild Solution for the 1D Vlasov-Poisson Initial-Boundary Value Problem

@article{Bostan2005ExistenceAU,
  title={Existence and Uniqueness of the Mild Solution for the 1D Vlasov-Poisson Initial-Boundary Value Problem},
  author={Mihai Bostan},
  journal={SIAM J. Math. Analysis},
  year={2005},
  volume={37},
  pages={156-188}
}
We prove the existence and uniqueness of the mild solution for the 1D Vlasov-Poisson system with initial-boundary conditions by using iterated approximations. The same arguments yield existence and uniqueness for the free space or space periodic system. The major difficulty is the treatment of the boundary conditions. The main idea consists of splitting the velocities range by introducing critical velocities corresponding to each boundary. One of the crucial points is to estimate the critical… CONTINUE READING

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