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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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Transformation from domains to half-spaces

The half spaces R^n are the inward-pointing halves of the tangent spaces to the points on the boundary. Starting with a local boundary value problem you end up with a model equation on the half space …
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