Abstract
In this paper by using anL ∞ estimate for elliptic equations, we study the well-posedness of the stationary semiconductor equations arising from modeling a nondestructive testing technique LBIC. It is shown that when the extra source term is small, the system has a unique weak solution, and the solution is continuously dependent on this source term. The validity of an approximate model derived for the study of the inverse problem is established. The existence result is then extended to the case of constant mobilities without the assumption on the size of the source term.
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Communicated by A. Bensoussan
Parts of this work were completed while the authors were members of the Center for Applied Mathematical Sciences at the University of Southern California, and was supported by Air Force Office of Scientific Research Grant AFOSR-90-0091.
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Fang, W., Ito, K. On the stationary semiconductor equations arising in modeling an LBIC technique. Appl Math Optim 33, 189–202 (1996). https://doi.org/10.1007/BF01183143
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DOI: https://doi.org/10.1007/BF01183143