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### Open Access Journals

We study detecting a boundary corrosion damage in the inaccessible part of a rectangular shaped electrostatic conductor from a one set of Cauchy data specified on an accessible boundary part of conductor. For this nonlinear ill-posed problem, we prove the uniqueness in a very general framework. Then we establish the conditional stability of Hölder type based on some *a priori* assumptions on the unknown impedance and the electrical current input specified in the accessible part. Finally a regularizing scheme of double regularizing parameters, using the truncation of the series expansion of the solution, is proposed with the convergence analysis on the explicit regularizing solution in terms of a practical average norm for measurement data.

We establish a regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity and vacuum in a bounded domain.

In this paper we study the low Mach number limit of the full compressible Hall-magnetohydrodynamic (Hall-MHD) system in $\mathbb{T}^3$. We prove that, as the Mach number tends to zero, the strong solution of the full compressible Hall-MHD system converges to that of the incompressible Hall-MHD system.

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