Variational formulation for a non-local elliptic problem in the theory of varistors

Abstract

The electric potential in a three-dimensional non-linear conductor of electricity in series with a one-dimensional resistor and a direct current generator is studied with a nonlocal elliptic problem. We give a variational formulation and a theorem of existence and uniqueness.

Keywords:

• varistor
• non-local problem
• existence
• uniqueness

AMS Subject Classifications::

• 35Q30
• 78D03