| Автор | Khapalov, Alexander |
| Дата выпуска | 1999 |
| dc.description | We consider the one dimensional semilinear reaction-diffusion equation, governed in Ω = (0,1) by controls, supported on any subinterval of (0, 1), which are the functions of time only. Using an asymptotic approach that we have previously introduced in [9], we show that such a system is approximately controllable at any time in both L <sup>2</sup>(0,1)( and C <sub>0</sub>[0,1], provided the nonlinear term f = f(x,t, u) grows at infinity no faster than certain power of log |u|. The latter depends on the regularity and structure of f (x, t, u) in x and t and the choice of the space for controllability. We also show that our results are well-posed in terms of the “actual steering” of the system at hand, even in the case when it admits non-unique solutions. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 1999 |
| Тема | The semilinear reaction-diffusion equation |
| Тема | approximate controllability |
| Тема | internal lumped control multiple solutions. |
| Название | Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls |
| Тип | research-article |
| DOI | 10.1051/cocv:1999104 |
| Electronic ISSN | 1262-3377 |
| Print ISSN | 1292-8119 |
| Журнал | ESAIM: Control, Optimisation and Calculus of Variations |
| Том | 4 |
| Первая страница | 83 |
| Последняя страница | 98 |
| Аффилиация | Khapalov Alexander; Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 99164-3113, USA; khapala@delta.math.wsu.edu. |
