Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation
Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation
摘要
The authors prove the global null controllability for the 1-dimensional nonlinear slow diffusion equation by using both a boundary and an internal control. They assume that the internal control is only time dependent. The proof relies on the return method in combination with some local controllability results for nondegenerate equations and rescaling techniques.
基金
Project supported by the ITN FIRST of the Seventh Framework Programme of the European Community (No. 238702)
the ERC advanced grant 266907 (CPDENL) of the 7th Research Framework Programme (FP7)
DGISPI of Spain (Project MTM2011-26119)
the Research Group MOMAT(No. 910480) supported by UCM
参考文献23
-
1Alt, H. W. and Luckhaus, S., Quasilinear elliptic-parabolic differential equations, Math. Z., 183(3), 1983, 311-341.
-
2Antontsev, S. N., Diaz, J. I. and Shmarev, S., Energy methods for free boundary problems, Applications to Nonlinear PDEs and Fluid Mechanics, Progress in Nonlinear Differential Equations and Their Applications, 48, Birkhauser Boston Inc., Boston, MA, 2002.
-
3Barenblatt, G. I., On some unsteady motions of a liquid and gas in a porous medium, Akad. Nauk SSSR. Prikl. Mat. Meh., 16, 1952, 67-68.
-
4Beceanu, M., Local exact controllability of the diffusion equation in one dimension, Abstr. Appl. Anal., 14, 2003, 793-711.
-
5Brezis, H., Proprietes r6gularisantes de certains semi-groupes non lin6aires, Israel J. Math., 9, 1971, 513- 534.
-
6Brezis, H., Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, Contributions to Non-linear Functional Analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971), Academic Press, New York, 1971, 101-156.
-
7Brezis, H., Operateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North Holland, Amsterdam, 1973.
-
8Chapouly, M., Global controllability of nonviscous and viscous Burgers-type equations, SIAM J. Control Optim., 48(3), 2009, 1567-1599.
-
9Coron, J. M., Global asymptotic stabilization for controllable systems without drift, Math. Control Signals Systems, 5(3), 1992, 295 312.
-
10Coron, J. M., On the controllability of 2-D incompressible perfect fluids, J. Math. Pures Appl. (9), 75(2), 1996, 155-188.
-
1YU Hang.Null controllability for a fourth order parabolic equation[J].Science in China(Series F),2009,52(11):2127-2132.
-
2Qi LU.Bang-Bang Principle of Time Optimal Controls and Null Controllability of Fractional Order Parabolic Equations[J].Acta Mathematica Sinica,English Series,2010,26(12):2377-2386. 被引量：2
-
3YANG Junhui and ZHAI QibinInstitute of Software , Chinese Academy of Sciences , Beijing 100080, China ,State Key Laboratory of Information Security , Beijing 100080, China.Nondegenerative ML-sequences over ring Z/(2~e)[J].Chinese Science Bulletin,1999,44(17):1557-1561.
-
4J. LIMACO,M. CLARK,A. MARINHO,S. B. de MENEZES,A. T. LOUREDO.Null Controllability of Some Reaction-Diffusion Systems with Only One Control Force in Moving Domains[J].Chinese Annals of Mathematics,Series B,2016,37(1):29-52.
-
5Hongheng LI,Qi LÜ.Null Controllability for Some Systems of Two Backward Stochastic Heat Equations with One Control Force[J].Chinese Annals of Mathematics,Series B,2012,33(6):909-918.
-
6吴相豪,李丽.海港码头混凝土构件氯离子浓度预测模型[J].上海海事大学学报,2006,27(1):17-20. 被引量：13
-
7孙忠强,方宝君.施工隧道内粉尘受力分析及其运动研究[J].煤炭技术,2016,35(5):176-178. 被引量：2
-
8王友生.返回法冶炼高锰钢辙叉氮气孔缺陷的预防[J].铸造技术,2004,25(10):789-790.
-
9李笃生.大客车空气悬架的构成及其特性分析[J].客车技术,2003(2):8-10.
-
10孙江,傅广生,苏红新,左战春,吴令安,傅盘铭.Three-Photon Resonant Nondegenerate Six-Wave Mixing in a Dressed Atomic System[J].Chinese Physics Letters,2008,25(10):3652-3655.
