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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.

4 votes
1 answer
331 views

Existence of solution for the PDE $p \frac{\partial f(p, q)}{\partial p}-q \frac{\partial f(...

Consider the following PDE: \begin{equation} p \frac{\partial f(p, q)}{\partial p}-q \frac{\partial f(p, q)}{\partial q}=g(p, q),\tag{$\star$} \end{equation} where $g$ is a flat function at the point …
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