Remarks on a 2-D nonlinear backward heat problem using a truncated Fourier series method.
Remarks on non controllability of the heat equation with memory
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.
Résolution numérique du problème de propagation de la chaleur à une dimension par la méthode itérative de sur-relaxation
Resolvent estimates in for discrete Laplacians on irregular meshes and maximum-norm stability of parabolic finite difference schemes.
Reverse convolution inequalities and applications to inverse heat source problems.
Riesz transform on manifolds and heat kernel regularity
Ritz Approximations to Two-Dimensional Boundary Value Problems.
Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients
In this work we derive a posteriori error estimates based on equations residuals for the heat equation with discontinuous diffusivity coefficients. The estimates are based on a fully discrete scheme based on conforming finite elements in each time slab and on the A-stable -scheme with . Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo 40 (2003) 195–212] it is easy to identify a time-discretization error-estimator and a space-discretization...
Robust a posteriori error estimates for finite element discretizations of the heat equation with discontinuous coefficients
In this work we derive a posteriori error estimates based on equations residuals for the heat equation with discontinuous diffusivity coefficients. The estimates are based on a fully discrete scheme based on conforming finite elements in each time slab and on the A-stable θ-scheme with 1/2 ≤ θ ≤ 1. Following remarks of [Picasso, Comput. Methods Appl. Mech. Engrg. 167 (1998) 223–237; Verfürth, Calcolo40 (2003) 195–212] it is easy to identify a time-discretization error-estimator and a space-discretization...
Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation.
Sets of determination for parabolic functions on a half-space
We characterize all subsets of such that for every bounded parabolic function on . The closely related problem of representing functions as sums of Weierstrass kernels corresponding to points of is also considered. The results provide a parabolic counterpart to results for classical harmonic functions in a ball, see References. As a by-product the question of representability of probability continuous distributions as sums of multiples of normal distributions is investigated.
Short-time heat flow and functions of bounded variation in
We prove a characterisation of sets with finite perimeter and functions in terms of the short time behaviour of the heat semigroup in . For sets with smooth boundary a more precise result is shown.
Simulation of continuously deforming parabolic problems by Galerkin finite-elements method.
Simultaneous versus nonsimultaneous blowup for a system of heat equations coupled boundary flux.
Singular and Quasi-Bounded Functions Associated with the Heat Equation.
Singularity of parabolic measures
Smooth solutions of the heat and wave equations.
Solvability of the heat equation in weighted Sobolev spaces
The existence of solutions to an initial-boundary value problem to the heat equation in a bounded domain in ℝ³ is proved. The domain contains an axis and the existence is proved in weighted anisotropic Sobolev spaces with weight equal to a negative power of the distance to the axis. Therefore we prove the existence of solutions which vanish sufficiently fast when approaching the axis. We restrict our considerations to the Dirichlet problem, but the Neumann and the third boundary value problems can...
Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes
A general class of nonconforming meshes has been recently studied for stationary anisotropic heterogeneous diffusion problems, see Eymard et al. (IMA J. Numer. Anal. 30 (2010), 1009–1043). Thanks to the basic ideas developed in the stated reference for stationary problems, we derive a new discretization scheme in order to approximate the nonstationary heat problem. The unknowns of this scheme are the values at the centre of the control volumes, at some internal interfaces, and at the mesh points...
Some new results related to the null controllability of the heat equation
We address three null controllability problems related to the heat equation. First we show that the heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation can be obtained...