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Milan Journal of Mathematics

, Volume 87, Issue 2, pp 283–301 | Cite as

Well-posedness of the Initial Value Problem for the Ostrovsky–Hunter Equation with Spatially Dependent Flux

  • G. M. Coclite
  • N. ChatterjeeEmail author
  • N. H. Risebro
Article
  • 15 Downloads

Abstract

In this paper we study the Ostrovsky–Hunter equation for the case where the flux function f(x, u) may depend on the spatial variable with certain smoothness. Our main results are that if the flux function is smooth enough (namely fx(x, u) is uniformly Lipschitz locally in u and fu(x, u) is uniformly bounded), then there exists a unique entropy solution. To show the existence, after proving some a priori estimates we have used the method of compensated compactness and to prove the uniqueness we have employed the method of doubling of variables.

Mathematics Subject Classification (2010)

Primary: 35L35 35G25 Secondary: 45M10 

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Meccanica, Matematica e ManagementPolitecnico di BariBariItaly
  2. 2.Department of MathematicsUniversity of OsloBlindernNorway

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