Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T18:43:38.070Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary and Interior Control for Partial Differential Equations

Published online by Cambridge University Press:  20 November 2018

Robert Delver
Robert Delver*
Affiliation:
University of Toronto, Toronto, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

From the time that the basic existence and regularity problems for partial differential equations have been solved many interesting new variational and control problems could be studied. In general a differential equation or boundary value problem is used to define a class of admissible functions, and then the problem is that of finding the extrema of a given functional defined on that class of functions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 200 - 217
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Agmon, S., Lectures on elliptic boundary value problems (D. Van Nostrand Company, Inc., New York, 1965).Google Scholar
2. Agmon, A., Douglis, A., and Nirenberg, L., Estimates near the boundary for the solutions of elliptic differential satisfying general boundary values. I, Comm. Pure Appl. Math. 12 (1959), 623–727.Google Scholar
3. Aronszajn, N. and Milgram, A. N., Differential operators on Riemannian manifolds, Rend. Circ. Mat. Palermo 2 (1953), 266–325.Google Scholar
4. Delver, R., The Optimization of a functional within the class of solutions of a partial differential equation, J. Engrg. Math. 4 (1969), 253–264.Google Scholar
5. Delver, R., Variational problems within the class of solutions of a partial differential equation, Bull. Amer. Math. Soc. 77 (1971), 1100–1105.Google Scholar
6. Delver, R., Variational problems within the class of solutions of a partial differential equation, Trans. Amer. Math. Soc. 180 (1973), 265–289.Google Scholar
7. Lions, J. L., Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles (Dunod et Gauthier-Villars, Paris, 1968).Google Scholar
8. Lions, J. L., $ur ie contrôle optimal de systèmes décrits par des equations aux dérivées partielles linéaires, C. R. Acad. Sci. Paris Sér. A-B, 263 (II) (1966), 713–715.Google Scholar
9. Lions, J. L. and Magenes, E., Equations différentielles opérationelles et problèmes aux limites, Vol. I (Dunod., Paris, 1968).Google Scholar
10. Friedman, A., Optimal control for parabolic equations, J. Math. Anal. Appl. 18 (1967), 479–491.Google Scholar
11. Friedman, A., Partial differential equation (Holt, Rinehart and Winston, New York, 1969).Google Scholar
12. Miranda, C., Equazioni aile derivate parziali di tipo ellittico, (Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 2, Springer-Verlag, Berlin, 1955); English transi., Springer-Verlag, Berlin, 1970.Google Scholar
13. Morrey, C. B., Jr., Multiple integrals in the calculus of variations (Springer-Verlag, New York Inc., 1966).Google Scholar