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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

In a paper I read, an elliptic boundary value problem on a bounded domain D x (0,T) is solved by first transforming it in a set of equations on half-spaces R^n and then applying partial Fourier transf …