Wave equation with an overdetermined boundary conditions, are there any results about its existence?

02 February 2016 1 5K Report

HI, I get a wave equation with mixed overdetermined boundary conditions. I want to know if there is any results about existence or non-existence?

NB: Read the attached file to see the full equation and boundary conditions.

Francis Collino

You cannot define both Dirichlet and Neumann conditions on Gamma_0.. Indeed, the Neumann value of your field on Gamma_0 is uniquely determined by the Neumann conditions on Sigma_pm and the condition u=0 on Gamma_0.

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