| 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 OPtim. Calc. Var. |
| 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 |