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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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Heat equation with Neumann BC

yes, with some regularity on the boundary. Theorem 3.2.9 p. 90 of E.B. Davies book, Heat Kernels and Spectral Theory gives Gaussian bounds for the heat kernel of an elliptic operator with Neumann bo …
Russell Brown's user avatar