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Physics
Classical Physics
Establishing linearity in laplace's equation with no closed-form solution
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[QUOTE="jdmo, post: 2841826, member: 191027"] I'm writing a paper, and as a motivation to the forthcoming finite element modeling, I want to state, with some sort of "proof" that Laplace's equation in a heterogeneous volume: \del (sigma \del V) = 0 exhibits linearity. By "linearity", I mean that if a set of initial conditions (call them I_1) lead to solution V_1, and another set of initial conditions (call them I_2) lead to solution V_2, then the solution to the equation with initial conditions I_1+I_2 is V_1+V_2. But I cannot do so in a straightforward manner because there is no closed-form solution which relates V_1 to I_1, for example. Is it enough just to say that Laplace's equation is linear and thus obeys superposition to initial conditions? I would like to make my claim more convincing. Thanks in advance. [/QUOTE]
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Classical Physics
Establishing linearity in laplace's equation with no closed-form solution
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