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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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Numerical analysis of parabolic obstacle problem

There's an overview of available schemes in chapter III of Roland Glowinski, MR 737005 Numerical methods for nonlinear variational problems, ISBN: 0-387-12434-9. (of which there is also reprint from …
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An acting condition for a superposition operator from $H^1(\Omega)$ to $H^1(\Omega)$

The following is stated in the paper Moshe Marcus and Victor J. Mizel, MR 531975 Complete characterization of functions which act, via superposition, on Sobolev spaces, Trans. Amer. Math. Soc. 251 (1 …
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