Geodesic
Piecewise Analytic Solutions of Mixed Boundary Value Problems
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1121-1147

Voir la notice de l'article provenant de la source Cambridge University Press

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). 
Eisen, M. Piecewise Analytic Solutions of Mixed Boundary Value Problems. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1121-1147. doi: 10.4153/CJM-1966-113-6
@article{10_4153_CJM_1966_113_6,
     author = {Eisen, M.},
     title = {Piecewise {Analytic} {Solutions} of {Mixed} {Boundary} {Value} {Problems}},
     journal = {Canadian journal of mathematics},
     pages = {1121--1147},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-113-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-113-6/}
}
TY  - JOUR
AU  - Eisen, M.
TI  - Piecewise Analytic Solutions of Mixed Boundary Value Problems
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 1121
EP  - 1147
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-113-6/
DO  - 10.4153/CJM-1966-113-6
ID  - 10_4153_CJM_1966_113_6
ER  - 
%0 Journal Article
%A Eisen, M.
%T Piecewise Analytic Solutions of Mixed Boundary Value Problems
%J Canadian journal of mathematics
%D 1966
%P 1121-1147
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-113-6/
%R 10.4153/CJM-1966-113-6
%F 10_4153_CJM_1966_113_6

[1] 1. Aitken, A. C., Determinants and matrices (London, 1951). Google Scholar

[2] 2. Campbell, L. L. and Robinson, A., Mixed problems for hyperbolic differential equations, Proc. Lond. Math. Soc, 18 (1956), 129–147. Google Scholar

[3] 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] 4. Duff, G. F. D., Mixed problems for linear systems of first order equations, Can. J. Math., 10 (1958), 127–160. Google Scholar

[5] 5. Duff, G. F. D., Mixed problems for hyperbolic equations of general order, Can. J. Math., 11 (1959), 195–222. Google Scholar

[6] 6. Goursat, E. and Hedrick, E. R., Mathematical analysis, Vol. 2, II (Boston, 1917). Google Scholar

[7] 7. Kryzyanski, M. and Schauder, J., Quasilineare Differentialgleichungen zweiter Ordnung vom hyperbolischen Typus, Gemischte Randwertaufgaben, Studia Math., 6 (1936), 152–189. Google Scholar

[8] 8. Ladyzhenskaya, O., Mixed problems for hyperbolic equations (Moscow, 1953). Google Scholar

[9] 9. Leray, J., Hyperbolic differential equations (Princeton, 1953). Google Scholar

[10] 10. Lions, J. L., Problèmes aux limites en théorie des distributions, Acta Math., 94 (1955), 13–153. Google Scholar

[11] 11. Lions, J. L., Opérateurs de Delsarte et problèmes mixtes, Bull, Soc. Math., 84 (1956), 9–95. Google Scholar

[12] 12. Petrowski, I. G., Lectures on partial differential equations (New York, 1954). Google Scholar

[13] 13. Van der Waerden, B. L., Modem algebra, Vol. II (New York, 1950). Google Scholar

Cité par Sources :