Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-25T12:57:36.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Mixed Problems for Linear Systems of first Order Equations

Published online by Cambridge University Press:  20 November 2018

G. F. D. Duff
G. F. D. Duff*
Affiliation:
University of Toronto
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.

A mixed problem in the theory of partial differential equations is an auxiliary data problem wherein conditions are assigned on two distinct surfaces having an intersection of lower dimension. Such problems have usually been formulated in connection with hyperbolic differential equations, with initial and boundary conditions prescribed. In this paper a study is made of the conditions appropriate to a system of R linear partial differential equations of first order, in R dependent and N independent variables.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 127 - 160
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Birkhoff, G. and MacLane, S., A Survey of Modern Algebra (New York, 1941).Google Scholar
2. Campbell, L. L. and Robinson, A. , Mixed problems for hyperbolic partial differential equations, Proc. Lond. Math. Soc. (3), 18 (1955), 129-147.Google Scholar
3. Duff, G. F. D., A mixed problem for normal hyperbolic linear partial differential equationsof second order, Can. J. Math., 9 (1957), 141-160.Google Scholar
4. Goursat, E. and Hedrick, E. R., Mathematical Analysis, Vol. II, Part II (Boston, 1917).Google Scholar
5. Graves, L. M., Theory of Functions of Real Variables (New York, 1946).Google Scholar
6. Friedrichs, K. O., Symmetric hyperbolic linear differential equations, Comm. Pure and App. Math., 7 (1954), 345-392.Google Scholar
7. Friedrichs, K. O. and Lewy, H., Ueber die Eindeutigkeit und die Abhangigkeitsgebiet der Losungen beim Anfangswertproblem linearer hyperbolischer Differentialgleichungen, Math. Ann., 28 (1927), 192-204.Google Scholar
8. Kryzyanski, M. and Schauder, J., Quasi linear e Differ entialgleichungen zweiter Ordnung vom hyperbolischen Typus, Gemischte Randwertaufgaben, Studia Math., 6 (1936), 152-189.Google Scholar
9. Ladyzhenskaya, O., Mixed Problems for Hyperbolic Equations (Moscow, 1953).Google Scholar
10. Leray, J., Hyperbolic Differential Equations (Princeton, 1953).Google Scholar
11. Lions, J. L., Problèmes aux limites en théorie des distributions, Acta Math., 94 (1955), 13– 153.Google Scholar
12. Lions, J. L., Opérateurs de Delsarte et problèmes mixtes, Bull. Soc. Math., 84 (1956), 9–95.Google Scholar
13. Lions, J. L., Quelques applications d'opérateurs de transmutation, Proc. Colloque internationale du C.N.R.S., 71 (1956), 125-137.Google Scholar
14. Petrowsky, I. G., Lectures on partial differential equations (trans.) (New York, 1954).Google Scholar
15. S. Sobolev, , Doklady, 10 (1936), 277-282.Google Scholar
16. Thomas, J. M., Riquiefs existence theorems, Ann. Math. (2), 30 (1929), 285-310; 35 (1934), 306-311.Google Scholar
17. van der Waerden, B. L., Moderne Algebra, Vol. II (Berlin, 1931).Google Scholar