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              <p>A conductive porous medium excited by a seismic wave is the scene of seismo-electric effects. Understanding them opens new prospects for imaging geological objects invisible to seismic imaging. This phenomenon has been modeled by Pride in the 90s, by a strong (two-way) coupling of Maxwell's (electromagnetics) with Biot's (porous elasticity) equations. A simplified system considering only Maxwell-to-Biot (electroseismic) or Biot-to-Maxwell (seismoelectric) coupling is often considered. In this context, it is enough to show existence and uniqueness of the solutions to the separate systems.We analyze the well-posedness of the boundary value problem resulting from strong Maxwell-Biot coupling. We consider the low-frequency regime which yields a constant coupling term and seek solutions in time domain. The main idea to prove the existence and uniqueness of the solution is to reformulate the considered Maxwell-Biot system such that the fixed-point theorem can be employed. Such a proof requires the derivation of various a priori estimates on both elastic and electromagnetic fields, that appear to be of general interest. Constraints on the physical parameters are respected for a quite general class of physical media.</p>
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