NULL CONTROLLABILITY FOR PARABOLIC OPERATORS WITH INTERIOR DEGENERACY AND ONE-SIDED CONTROL

被引：12

作者：

Cannarsa, Piermarco ^{[1
]}

Ferretti, Roberto ^{[2
]}

Martinez, Patrick ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Univ Roma Tre, Dipartimento Matemat & Fis, Lgo S Leonardo Murialdo 1, I-00146 Rome, Italy

[3] Univ Paul Sabatier Toulouse III, Inst Math Toulouse, UMR CNRS 5219, F-31062 Toulouse 4, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2019年 / 57卷 / 02期

关键词：

degenerate parabolic equations; null controllability; spectral problem; Bessel functions; EQUATIONS; COST;

D O I：

10.1137/18M1198442

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

For alpha is an element of (0, 2) we study the null controllability of the parabolic operator Pu = u(t) - (vertical bar x vertical bar(alpha)ux)(x) (-1 < x < 1), which degenerates at the interior point x = 0 for locally distributed controls acting only on one side of the origin (that is, on some interval (a, b) with 0 < a < b < 1). Our main results guarantee that P is null controllable if and only if it is weakly degenerate, that is, alpha is an element of (0, 1). (So, in order to steer the system to zero, one needs controls to act on both sides of the point of degeneracy in the strongly degenerate case alpha is an element of [1, 2).) Our approach is based on spectral analysis and the moment method. We also provide numerical evidence to illustrate our theoretical results.

引用

页码：900 / 924

页数：25

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