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PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages

Fredi Tröltzsch, Irwin Yousept (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with a PDE-constrained optimization problem of induction heating, where the state equations consist of 3D time-dependent heat equations coupled with 3D time-harmonic eddy current equations. The control parameters are given by finite real numbers representing applied alternating voltages which enter the eddy current equations via impressed current. The optimization problem is to find optimal voltages so that, under certain constraints on the voltages and the temperature, a...

PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages

Fredi Tröltzsch, Irwin Yousept (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with a PDE-constrained optimization problem of induction heating, where the state equations consist of 3D time-dependent heat equations coupled with 3D time-harmonic eddy current equations. The control parameters are given by finite real numbers representing applied alternating voltages which enter the eddy current equations via impressed current. The optimization problem is to find optimal voltages so that, under certain constraints on the voltages and the temperature, a...

Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems

Mihai Bostan, Eric Sonnendrücker (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the existence of spatial periodic solutions for nonlinear elliptic equations - Δ u + g ( x , u ( x ) ) = 0 , x N where g is a continuous function, nondecreasing w.r.t. u . We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions g are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations....

Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems

Mihai Bostan, Eric Sonnendrücker (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We study the existence of spatial periodic solutions for nonlinear elliptic equations - Δ u + g ( x , u ( x ) ) = 0 , x N where g is a continuous function, nondecreasing w.r.t. u. We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions g are investigated as well. As an application we analyze the mathematical model of electron beam focusing system and we prove the existence of positive periodic solutions for the envelope equation. We present also numerical simulations. ...

Poisson-Boltzmann equation in ℝ³

A. Krzywicki, T. Nadzieja (1991)

Annales Polonici Mathematici

The electric potential u in a solute of electrolyte satisfies the equation Δu(x) = f(u(x)), x ∈ Ω ⊂ ℝ³, u | Ω = 0 . One studies the existence of a solution of the problem and its properties.

Propagation of electromagnetic waves in non-homogeneous media

Radjesvarane Alexandre, Hassan Taha (2004)

Applications of Mathematics

We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.

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