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cianfa72

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- About the interdependence of Maxwell's equations from the point of view of PDE theory

Hi, as in this thread Are maxwells equations linearly dependent I would like to better understand from a mathematical point of view the interdependence of Maxwell's equations.

Maxwell's equations are solved assuming as

From Partial Derivatives Equations (PDE) theory are the above conditions actually necessary and sufficient to uniquely define an unique solution?

Thanks.

Maxwell's equations are solved assuming as

*given/fixed*the charge density ##\rho## and the current density ##J## as functions of ##(x,y,z,t)##. Therefore one can freely assign both ##\rho(x,y,z,t)## and ##J(x,y,z,t)## as long as the continuity condition is fulfilled: $$\nabla \cdot J = - \frac {\partial \rho} {\partial t}$$ The 4 Maxwell's PDE equations put conditions on divergence and curl of ##E## and ##B## vector fields.From Partial Derivatives Equations (PDE) theory are the above conditions actually necessary and sufficient to uniquely define an unique solution?

Thanks.

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