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Inventiones mathematicae

, Volume 98, Issue 3, pp 511–547 | Cite as

Ordinary differential equations, transport theory and Sobolev spaces

  • R. J. DiPerna
  • P. L. Lions
Article

Summary

We obtain some new existence, uniqueness and stability results for ordinary differential equations with coefficients in Sobolev spaces. These results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions.

Keywords

Differential Equation Ordinary Differential Equation Sobolev Space Transport Equation Stability Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    DiPerna, R.J., Lions, P.L.: On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. Math. (to appear); see also C.R. Acad. Sci. Paris306, 343–346, (1988) and In Séminaire EDP, Ecole Polytechnique, 1987–88, PalaiseauGoogle Scholar
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    DiPerna, R.J., Lions, P.L.: Global weak solutions of Vlasov Maxwell systems. Commun. Phys. Appl. Math. (to appear)Google Scholar
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    DiPerna, R.J., Lions, P.L.: In preparation, see also C.R. Acad. Sci. Paris307, 655–658 (1988)Google Scholar
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    DiPerna, R.J., Lions, P.L.: In preparation, see also in Séminaire EDP, Ecole Polytechnique, 1988–89, PalaiseauGoogle Scholar
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    DiPerna, R.J., Lions, P.L.: In preparation, see also in Séminaire EDP, Ecole Polytechnique, 1988–89, PalaiseauGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • R. J. DiPerna
    • 1
  • P. L. Lions
    • 2
  1. 1.Department of MathematicsUniversity of BerkeleyBerkeleyUSA
  2. 2.CeremadeUniversité de Paris-DauphineParis Cedex 16France

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