Solutions in the large for multi-dimensional non linear partial differential equations of first order
Annales de l'Institut Fourier, Volume 15 (1965) no. 2, pp. 1-35.

Une solution d’une équation différentielle partielle non-linéaire du premier ordre peut espérer avoir des dérivées continues seulement dans un domaine limité, dépendant de la solution elle-même. Des solutions absolument continues satisfaisant l’équation différentielle presque partout n’ont pas besoin cependant d’être similairement limitées, quant au domaine. L’intérêt de cet article est la détermination continue unique de solutions absolument continues par leurs données initiales.

@article{AIF_1965__15_2_1_0,
     author = {Douglis, Avron},
     title = {Solutions in the large for multi-dimensional non linear partial differential equations of first order},
     journal = {Annales de l'Institut Fourier},
     pages = {1--35},
     publisher = {Institut Fourier},
     volume = {15},
     number = {2},
     year = {1965},
     doi = {10.5802/aif.208},
     zbl = {0137.29001},
     mrnumber = {33 #7686},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.208/}
}
TY  - JOUR
AU  - Douglis, Avron
TI  - Solutions in the large for multi-dimensional non linear partial differential equations of first order
JO  - Annales de l'Institut Fourier
PY  - 1965
DA  - 1965///
SP  - 1
EP  - 35
VL  - 15
IS  - 2
PB  - Institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.208/
UR  - https://zbmath.org/?q=an%3A0137.29001
UR  - https://www.ams.org/mathscinet-getitem?mr=33 #7686
UR  - https://doi.org/10.5802/aif.208
DO  - 10.5802/aif.208
LA  - en
ID  - AIF_1965__15_2_1_0
ER  - 
%0 Journal Article
%A Douglis, Avron
%T Solutions in the large for multi-dimensional non linear partial differential equations of first order
%J Annales de l'Institut Fourier
%D 1965
%P 1-35
%V 15
%N 2
%I Institut Fourier
%U https://doi.org/10.5802/aif.208
%R 10.5802/aif.208
%G en
%F AIF_1965__15_2_1_0
Douglis, Avron. Solutions in the large for multi-dimensional non linear partial differential equations of first order. Annales de l'Institut Fourier, Volume 15 (1965) no. 2, pp. 1-35. doi : 10.5802/aif.208. http://www.numdam.org/articles/10.5802/aif.208/

[1] A. Douglis, On discontinuous initial value problems for certain non-linear partial differential equations, Tech. Note BN-119, AFOSR-TN-58-165, AD-152 192, Univ. of Md., Feb., 1958, 1-25. | Zbl

[2] A. Douglis, On calculating weak solutions of quasi-linear, first-order partial differential equations, Contributions to Differential Equations, 1 (1963), 59-94. | Zbl

[3] P. D. Lax, Weak solutions of non-linear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math., 7 (1954), 159-193. | Zbl

[4] O. A. Oleinik, Discontinuous solutions of non linear differential equations, Uspekhi Mat. Nauk, 12 (1957), 3-73. | Zbl

[5] C. Pucci, Compatezza di successioni di funzioni e derivibilita delle funzioni limiti, Ann. Mat. Pura ed Appl., 4 (1954), 1-25. | Zbl

[6] B. L. Rozhdestvenskii, Discontinuous solutions of hyperbolic systems of quasi-linear equations, Uspekhi Mat. Nauk, 15 (1960),n° 6 (96), 59-117 (Russian), translated as Russian Math. Surveys, 15 (1960),n° 6, 53-111. | Zbl

[7] N. D. Vvedenskaya, The difference method solution of Cauchy's problem for a non-linear equation with discontinuous initial values, Doklady Akad. Nauk SSSR, 111 (1956), 517-521. | Zbl

Cited by Sources: