
Approximation of exact controls for semilinear 1D wave equations using a leastsquares approach
The exact distributed controllability of the semilinear wave equation y_...
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Numerical computation of Neumann controllers for the heat equation on a finite interval
This paper presents a new numerical method which approximates Neumann ty...
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Variants of the Finite Element Method for the Parabolic Heat Equation: Comparative Numerical Study
Different variants of the method of weighted residual finite element met...
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Mean value methods for solving the heat equation backwards in time
We investigate an iterative mean value method for the inverse (and highl...
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Speed of convergence of Chernoff approximations for two model examples: heat equation and transport equation
Paul Chernoff in 1968 proposed his approach to approximations of onepar...
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A masslumping finite element method for radially symmetric solution of a multidimensional semilinear heat equation with blowup
This study presents a new masslumping finite element method for computi...
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On generating fully discrete samples of the stochastic heat equation on an interval
Generalizing an idea of Davie and Gaines (2001), we present a method for...
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Approximation of null controls for semilinear heat equations using a leastsquares approach
The null distributed controllability of the semilinear heat equation y_tΔ y + g(y)=f 1_ω, assuming that g satisfies the growth condition g(s)/( slog^3/2(1+ s))→ 0 as  s→∞ and that g^'∈ L^∞_loc(ℝ) has been obtained by FernándezCara and Zuazua in 2000. The proof based on a fixed point argument makes use of precise estimates of the observability constant for a linearized heat equation. It does not provide however an explicit construction of a null control. Assuming that g^'∈ W^s,∞(ℝ) for one s∈ (0,1], we construct an explicit sequence converging strongly to a null control for the solution of the semilinear equation. The method, based on a leastsquares approach, generalizes Newton type methods and guarantees the convergence whatever be the initial element of the sequence. In particular, after a finite number of iterations, the convergence is super linear with a rate equal to 1+s. Numerical experiments in the one dimensional setting support our analysis.
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