Is a solution of a differential equation a function of its parameters?

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  • #1
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Hi everyone,

Imagine I have a system of linear differential equations, e.g. the Maxwell equations.

Imagine my input variables are the conductivity $\sigma$. Is it correct from the mathematical point of view to say that the electric field solution, $E$, is a function of sigma in general, E(r,t,sigma)?

Thank you
 

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  • #2
pasmith
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Yes. Unless something weird is going on, the value of the solution at a particular point and time is determined by the parameters and the initial and boundary conditions.
 
  • #3
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Yes. Unless something weird is going on, the value of the solution at a particular point and time is determined by the parameters and the initial and boundary conditions.

Thank you
 
  • #4
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Basically, any differential equation describes a family of curves, surfaces, volumes...

It's the boundary conditions and initial parameters that fix it to one curve, surface or volume...
 

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