## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
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DCDS

In this paper we introduce an obstacle thermistor system. The existence
of weak solutions to the steady-state systems and capacity solutions to the time dependent
systems are obtained by a penalized method under reasonable assumptions
for the initial and boundary data. At the same time, we prove that there exists
a uniform absorbing set for nonnegative initial data in $L_2(\Omega)$. Finally for smooth
initial data a global attractor to the system is obtained by a series of Campanato
space arguments.

DCDS-B

In this paper we consider a thermistor problem with a current source,
i.e., a nonlocal boundary condition. The electric potential is unknown on part of the
boundary, but the current through it is known. We apply a decomposition technique
and transform the equation satisfied by the potential into two elliptic problems with
usual boundary conditions. The unique solvability of the initial boundary value
problem is achieved.

DCDS-B

In this paper we study a box scheme (or finite volume element method) for a
non-local nonlinear parabolic variational inequality arising in the study
of thermistor problems. Under some assumptions on
the data and regularity of the solution, optimal error estimates in the
$H^1$-norm are attained.

## Year of publication

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