Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-21T19:21:57.786Z Has data issue: false hasContentIssue false
  • English
  • Français

Piecewise Analytic Solutions of Mixed Boundary Value Problems

Published online by Cambridge University Press:  20 November 2018

M. Eisen
M. Eisen*
Affiliation:
University of Pittsburgh
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.

In a mixed problem one is required to find a solution of a system of partial differential equations when the values of certain combinations of the derivatives are given on two or more distinct intersecting surfaces. If the differential equations arise from some physical process, the correct boundary conditions are usually apparent. Many particular problems of this type have been solved by special methods such as separation of variables and the method of images. However, no general criterion has been given for what constitutes a correctly set mixed problem. In fact such problems have usually been formulated in connection with hyperbolic differential equations with data prescribed on two surfaces (called the initial and boundary surfaces).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1121 - 1147
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Aitken, A. C., Determinants and matrices (London, 1951).Google Scholar
2. Campbell, L. L. and Robinson, A., Mixed problems for hyperbolic differential equations, Proc. Lond. Math. Soc, 18 (1956), 129–147.Google Scholar
3. Duff, G. F. D., A mixed problem for normal hyperbolic linear partial differential equations of second order, Can. J. Math., 9 (1957), 141–160.Google Scholar
4. Duff, G. F. D., Mixed problems for linear systems of first order equations, Can. J. Math., 10 (1958), 127–160.Google Scholar
5. Duff, G. F. D., Mixed problems for hyperbolic equations of general order, Can. J. Math., 11 (1959), 195–222.Google Scholar
6. Goursat, E. and Hedrick, E. R., Mathematical analysis, Vol. 2, II (Boston, 1917).Google Scholar
7. Kryzyanski, M. and Schauder, J., Quasilineare Differentialgleichungen zweiter Ordnung vom hyperbolischen Typus, Gemischte Randwertaufgaben, Studia Math., 6 (1936), 152–189.Google Scholar
8. Ladyzhenskaya, O., Mixed problems for hyperbolic equations (Moscow, 1953).Google Scholar
9. Leray, J., Hyperbolic differential equations (Princeton, 1953).Google Scholar
10. Lions, J. L., Problèmes aux limites en théorie des distributions, Acta Math., 94 (1955), 13–153.Google Scholar
11. Lions, J. L., Opérateurs de Delsarte et problèmes mixtes, Bull, Soc. Math., 84 (1956), 9–95.Google Scholar
12. Petrowski, I. G., Lectures on partial differential equations (New York, 1954).Google Scholar
13. Van der Waerden, B. L., Modem algebra, Vol. II (New York, 1950).Google Scholar