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Radiative Heating of a Glass Plate

Luc Paquet, Raouf El Cheikh, Dominique Lochegnies, Norbert Siedow (2012)

MathematicS In Action

This paper aims to prove existence and uniqueness of a solution to the coupling of a nonlinear heat equation with nonlinear boundary conditions with the exact radiative transfer equation, assuming the absorption coefficient κ ( λ ) to be piecewise constant and null for small values of the wavelength λ as in the paper of N. Siedow, T. Grosan, D. Lochegnies, E. Romero, “Application of a New Method for Radiative Heat Tranfer to Flat Glass Tempering”, J. Am. Ceram. Soc., 88(8):2181-2187 (2005). An important...

Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates

Marián Slodička (2003)

Applications of Mathematics

In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain Ω ⊂ ℝ N , with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant α ( t ) , accompanied with a nonlocal (integral) Dirichlet side condition. We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution u and...

Regional boundary observability: a numerical approach

El Hassane Zerrik, Hamid Bourray, Ali Boutoulout (2002)

International Journal of Applied Mathematics and Computer Science

In this paper we review the concept of regional boundary observability, developed in (Michelitti, 1976), by means of sensor structures. This leads to the so-called boundary strategic sensors. A characterization of such sensors which guarantees regional boundary observability is given. The results obtained are applied to a two-dimensional system, and various cases of sensors are considered. We also describe an approach which leads to the estimation of the initial boundary state, which is illustrated...

Regularity for entropy solutions of a class of parabolic equations with irregular data

Fengquan Li (2007)

Commentationes Mathematicae Universitatis Carolinae

Using as a main tool the time-regularizing convolution operator introduced by R. Landes, we obtain regularity results for entropy solutions of a class of parabolic equations with irregular data. The results are obtained in a very general setting and include known previous results.

Remarks on non controllability of the heat equation with memory

Sergio Guerrero, Oleg Yurievich Imanuvilov (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.

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