Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Generic heat diffusion is scalar controllable


Author: Lawrence Markus
Journal: Proc. Amer. Math. Soc. 114 (1992), 261-262
MSC: Primary 93B05; Secondary 35K57, 58G30, 93C20
MathSciNet review: 1056681
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The partial differential equation for heat diffusion on a closed manifold $ M$ is approximately controllable by a single distributed controller, under generic conditions. But we also give examples, where $ M$ is a torus surface, for which no finite number of scalar controllers suffice.


References [Enhancements On Off] (What's this?)

  • [1] H. O. Fattorini, On complete controllability of linear systems, J. Differential Equations 3 (1967), 391–402. MR 0212322
  • [2] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
  • [3] Lawrence Markus, Introduction to the theory of distributed control systems, Distributed parameter control systems (Minneapolis, MN, 1989) Lecture Notes in Pure and Appl. Math., vol. 128, Dekker, New York, 1991, pp. 1–60. MR 1108854
  • [4] K. Uhlenbeck, Generic properties of eigenfunctions, Amer. J. Math. 98 (1976), no. 4, 1059–1078. MR 0464332

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 93B05, 35K57, 58G30, 93C20

Retrieve articles in all journals with MSC: 93B05, 35K57, 58G30, 93C20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1056681-0
Article copyright: © Copyright 1992 American Mathematical Society