Boundary-value problems for an equation of Keldysh type
نویسنده
چکیده
We prove the existence of strong solutions to a class of inhomogeneous boundary-value problems for an elliptic-hyperbolic equation. The equation is an arbitrarily small lower-order perturbation of an equation that arises in the linearization of an approximate model for high-frequency waves near a caustic. The domain boundary is allowed to extend into both the elliptic and hyperbolic regions of the equation, which makes the classical Dirichlet problem ill-posed on the hyperbolic portion of the boundary. However, the perturbed equation is strongly well-posed even if data are prescribed on both the elliptic and hyperbolic boundaries.
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