It is by now well known that the use of Carleman estimates allows to establish the controllability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is indeed reachable. In this paper, we pursue the study of the reachable states of parabolic equations based on a direct approach using control inputs in Gevrey spaces by considering a semilinear heat equation in dimension one. The nonlinear part is assumed to be an analytic function of the spatial variable x, the unknown y, and its derivative
Mots-clés : Semilinear heat equation, Exact controllability, Ill-posed problems, Gevrey class, Reachable states
@article{AIHPC_2020__37_4_1047_0, author = {Laurent, Camille and Rosier, Lionel}, title = {Exact controllability of semilinear heat equations in spaces of analytic functions}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1047--1073}, publisher = {Elsevier}, volume = {37}, number = {4}, year = {2020}, doi = {10.1016/j.anihpc.2020.03.001}, mrnumber = {4104834}, zbl = {1448.93030}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.anihpc.2020.03.001/} }
TY - JOUR AU - Laurent, Camille AU - Rosier, Lionel TI - Exact controllability of semilinear heat equations in spaces of analytic functions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2020 SP - 1047 EP - 1073 VL - 37 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2020.03.001/ DO - 10.1016/j.anihpc.2020.03.001 LA - en ID - AIHPC_2020__37_4_1047_0 ER -
%0 Journal Article %A Laurent, Camille %A Rosier, Lionel %T Exact controllability of semilinear heat equations in spaces of analytic functions %J Annales de l'I.H.P. Analyse non linéaire %D 2020 %P 1047-1073 %V 37 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2020.03.001/ %R 10.1016/j.anihpc.2020.03.001 %G en %F AIHPC_2020__37_4_1047_0
Laurent, Camille; Rosier, Lionel. Exact controllability of semilinear heat equations in spaces of analytic functions. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 4, pp. 1047-1073. doi : 10.1016/j.anihpc.2020.03.001. https://www.numdam.org/articles/10.1016/j.anihpc.2020.03.001/
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