Uniform asymptotic error estimates for semiconductor device and electrochemistry equations

Abstract

Abstract The paper is organized as follows. Section 1 sets up the problem, our purpose and results and the existing results in the literature. Section 2 gives the notations used in the paper. Sections 3 and 4 set up the problem in the case of a symmetric piecewise constant junction and recall the associated asymptotic expansion. In Section 5 our method is introduced and uniform asymptotic error estimates for a symmetric piecewise constant junction are derived. Section 6 is an application of our technique for the case of a biological membrane with a constant concentration of fixed charges. Uniform asymptotic error estimates are also proved to hold in that case. A brief summary and conclusion are given. In the appendix we give the proofs of the lemmas which are used in Sections 5 and 6.