Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The space charge problem and the nonlinear resistor

Author: Giovanni Cimatti
Journal: Quart. Appl. Math. 74 (2016), 49-59
MSC (2010): Primary 35J66, 35J75, 78M35
DOI: https://doi.org/10.1090/qam/1422
Published electronically: December 3, 2015
MathSciNet review: 3472519
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Abstract | References | Similar Articles | Additional Information

Abstract: We propose the constitutive equation $ \mathbf {J}=f(q)\mathbf {E}$, where $ \mathbf {J}$ is the current density, $ q$ the charge density, $ \mathbf {E}$ the electric field and $ f(q)$ a given function to describe the current-voltage laws appearing in certain special materials. A theorem of existence and uniqueness of solution is also given for the related nonlinear boundary value problem.

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Additional Information

Giovanni Cimatti
Affiliation: Department of Mathematics, Largo Bruno Pontecorvo, 5, 56100 Pisa, Italy
Email: cimatti@dm.unipi.it

DOI: https://doi.org/10.1090/qam/1422
Received by editor(s): April 18, 2014
Received by editor(s) in revised form: October 22, 2014
Published electronically: December 3, 2015
Article copyright: © Copyright 2015 Brown University

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