Determining a pair of metrics by boundary energy associated to a multitime PDE system

  • Authors:

  • Ariana Pitea;Constantin Udriste

  • Affiliations:

  • Faculty of Applied Sciences, Department of Mathematics I, University Politehnica of Bucharest, Bucharest, Romania;Faculty of Applied Sciences, Department of Mathematics I, University Politehnica of Bucharest, Bucharest, Romania

  • Venue:
  • WSEAS Transactions on Mathematics
  • Year:
  • 2008

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Abstract

Our theory of determining a tensor by boundary energy of a multitime first order PDE system is similar to those developed by Sharafutdinov. Section 1 refines the theory of potential maps determined by a first order multitime PDE system and a vertical metric. Section 2 defines the boundary energy of a first order PDE system and proves that the problem of determining a vertical metric from the boundary energy of a multitime PDE system cannot have a unique solution. Section 3 linearizes the above mentioned problem and defines the notion of multi-ray transform.