Complex coupled problems are mathematical models of physical systems (or physically motivated problems) which are governed by partial differential equations and which involve multiple components, complex physics or multi-physics, as well as complex or coupled domains, or multiple scales. One such phenomenon is electroporoelasticity.
After introducing the equations of electroporoelasticity (the equations of poroelasticity coupled to Maxwell's equations) which have applications in geoscience, hydrology, and petroleum exploration, as well as various areas of science and technology, I will describe some recent results (well posedness), the numerical analysis of a finite-element based method for approximating solutions, and some challenges.
A. J. Meir is a professor of mathematics at Southern Methodist University. He received his Ph.D. in mathematics from Carnegie Mellon University and B.Sc. in aeronautical engineering from the Technion — Israel Inst. of Technology.
Before joining SMU he was a professor of mathematics at Auburn University and also served as a rotator, program director, at NSF (DMS Computational Mathematics). In his old age, he has developed an interest, some say obsession, with n-ary, puzzles, of which the Chinese Ring Puzzle (Baguenaudier; 2-ary), and Towers of Hanoi (3-ary) are some of the most familiar.