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Neumann boundary condition for a non-autonomous Hamilton-Jacobi equation in a quarter plane

Author

Listed:
  • Adimurthi

    (T.I.F.R. Centre for Applicable Mathematics)

  • G. D. Veerappa Gowda

    (T.I.F.R. Centre for Applicable Mathematics)

Abstract

We consider Hamilton-Jacobi equation u t +H(u, u x ) = 0 in the quarter plane and study initial boundary value problems with Neumann boundary condition on the line x = 0. We assume that p → H(u, p) is convex, positively homogeneous of degree one. In general, this problem need not admit a continuous viscosity solution when s → H(s, p) is non increasing. In this paper, explicit formula for a viscosity solution of the initial boundary value problem is given for the cases s → H(s, p) is non decreasing as well as s → H(s, p) is non increasing.

Suggested Citation

  • Adimurthi & G. D. Veerappa Gowda, 2010. "Neumann boundary condition for a non-autonomous Hamilton-Jacobi equation in a quarter plane," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(1), pages 199-224, February.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:1:d:10.1007_s13226-010-0001-5
    DOI: 10.1007/s13226-010-0001-5
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