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Results tagged with ap.analysis-of-pdes
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user 93816
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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Solving a system of Laplace equations
Let $u_0$ and $u_1$ to be smooth functions defined on $\Omega\subset\mathbb{R}^n$, consider the following system of equations
$$\triangle u_1 = C_1(\partial_{ij}u_0),$$
$$\triangle u_0 = C_0u_1,$$
w …
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