| Title |
Approximation of null controls for semilinear heat equations using a least-squares approach |
| Authors |
Lemoine, Jerome , MARÍN GAYTE, IRENE, Munch, Arnaud |
| External publication |
Si |
| Means |
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS |
| Scope |
Article |
| Nature |
Científica |
| JCR Quartile |
2 |
| SJR Quartile |
1 |
| JCR Impact |
1.708 |
| SJR Impact |
1.015 |
| Publication date |
22/06/2021 |
| ISI |
000664960200001 |
| DOI |
10.1051/cocv/2021062 |
| Abstract |
The null distributed controllability of the semilinear heat equation partial differential (t)y - Delta y + g(y) = f 1(omega) assuming that g is an element of C-1(DOUBLE-STRUCK CAPITAL R) satisfies the growth condition lim sup(|r|->infinity)g(r)/(|r|ln(3/2)|r|) = 0 has been obtained by Fernandez-Cara and Zuazua (2000). The proof based on a non constructive fixed point theorem makes use of precise estimates of the observability constant for a linearized heat equation. Assuming that g \' is bounded and uniformly Holder continuous on DOUBLE-STRUCK CAPITAL R with exponent p is an element of (0, 1], we design a constructive proof yielding an explicit sequence converging strongly to a controlled solution for the semilinear equation, at least with order 1 + p after a finite number of iterations. The method is based on a least-squares approach and coincides with a globally convergent damped Newton method: it guarantees the convergence whatever be the initial element of the sequence. Numerical experiments in the one dimensional setting illustrate our analysis. |
| Keywords |
Semilinear heat equation; null controllability; least-squares method |
| Universidad Loyola members |
|
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