If a is the identity map,(1.1) is proposed in [C] as a model for the electrical heating of a
conductor. In this situation, u is the temperature of the conductor and p the electric potential …

We study an optimal control problem associated to a fractional nonlocal thermistor problem
involving the ABC (Atangana–Baleanu–Caputo) fractional time derivative. We first prove the …

This paper studies the system (∂/∂t)α(u)-div\,a(∇u)∋σ(u)|∇φ|^2, div\,(σ(u)∇φ)=0 in a
bounded domain of R^N coupled with initial and boundary conditions. Here, α is a maximal …

In this paper we investigate quasilinear systems of reaction-diffusion equations with mixed
Dirichlet–Neumann boundary conditions on nonsmooth domains. Using techniques from …

In this paper, the superclose and superconvergence analysis of the nonlinear time-fractional
thermistor problem are investigated by bilinear finite element method (FEM) for a fully …

We perform some 3D numerical experiments for the approximation of the solutions to a bead
type thermistor problem. We consider the case of a diagonal anisotropic diffusion matrix …

We consider the system (∂/∂ t) u=∆ u+ σ (u)|∇ φ| 2, div (σ (u)∇ φ)= 0 in a bounded region
of ℝN coupled with initial and boundary conditions, where σ (s)∈ C (ℝ) is nonnegative and …

We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal
parabolic equation resulting from thermistor problem. Our approach is based on the …

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 …

A partial regularity theorem is established for weak solutions of elliptic equations of the form
div(A(y)∇ψ)=0. Here we allow the possibility that the eigenvalues of A(y) are not bounded …