{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T09:51:30Z","timestamp":1775814690634,"version":"3.50.1"},"reference-count":8,"publisher":"American Mathematical Society (AMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>\n                    It is proved that if a generalized Goursat-Darboux problem is\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper C Superscript normal infinity\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>C<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"normal\">\n                                \u221e\n                                \n                              <\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">C^{\\infty }<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -well posed then the operator cannot contain derivatives with respect to one of the variables.\n                  <\/p>","DOI":"10.1090\/s0002-9939-97-03684-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:16:47Z","timestamp":1027707407000},"page":"471-475","source":"Crossref","is-referenced-by-count":6,"special_numbering":"452","title":["The generalized Goursat-Darboux problem for a third order operator"],"prefix":"10.1090","volume":"125","author":[{"given":"Jaime","family":"Silva","sequence":"first","affiliation":[]},{"given":"Carlos","family":"Leal","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1997,2]]},"reference":[{"issue":"6","key":"1","first-page":"223","article-title":"Probl\u00e8me de Goursat-Darboux g\u00e9n\u00e9ralis\u00e9 pour un op\u00e9rateur du troisi\u00e8me ordre","volume":"303","author":"Carvalho e Silva, Jaime","year":"1986","journal-title":"C. R. Acad. Sci. Paris S\\'{e}r. I Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0249-6291","issn-type":"print"},{"key":"2","unstructured":"\\bysame, On the hyperbolicity of a third order operator and the generalized Goursat-Darboux problem, Portugaliae Mathematica, 46 Sup, 1989, pp. 567\u2013577."},{"key":"3","unstructured":"\\bysame, Asymptotic representations for some multiple hypergeometric functions, Publica\u00e7\u00f5es de F\u00edsica-Matem\u00e1tica, no. 5, 1986, pp. 26\u201345."},{"issue":"7","key":"4","first-page":"516","article-title":"On the \ud835\udc36^{\u221e}-Goursat problem for 2nd order equations with real constant coefficients","volume":"51","author":"Hasegawa, Yukiko","year":"1975","journal-title":"Proc. Japan Acad.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-4280","issn-type":"print"},{"key":"5","series-title":"Mathematics in Science and Engineering, Vol. 53","volume-title":"The special functions and their approximations, Vol. I","author":"Luke, Yudell L.","year":"1969"},{"key":"6","volume-title":"The theory of partial differential equations","author":"Mizohata, Sigeru","year":"1973"},{"key":"7","doi-asserted-by":"crossref","first-page":"225","DOI":"10.5802\/aif.215","article-title":"Caract\u00e9ristiques multiples et bicaract\u00e9ristiques des syst\u00e8mes d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles lin\u00e9aires et \u00e0 coefficients constants","volume":"15","author":"Vaillant, Jean","year":"1965","journal-title":"Ann. Inst. Fourier (Grenoble)","ISSN":"https:\/\/id.crossref.org\/issn\/0373-0956","issn-type":"print"},{"key":"8","first-page":"1","article-title":"Donn\u00e9es de Cauchy port\u00e9es par une caract\u00e9ristique double, dans le cas d\u2019un syst\u00e8me lin\u00e9aire d\u2019\u00e9quations aux d\u00e9riv\u00e9es partielles, r\u00f4le des bicaract\u00e9ristiques","volume":"47","author":"Vaillant, Jean","year":"1968","journal-title":"J. Math. Pures Appl. (9)","ISSN":"https:\/\/id.crossref.org\/issn\/0021-7824","issn-type":"print"}],"container-title":["Proceedings of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/proc\/1997-125-02\/S0002-9939-97-03684-8\/S0002-9939-97-03684-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/proc\/1997-125-02\/S0002-9939-97-03684-8\/S0002-9939-97-03684-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T09:01:43Z","timestamp":1775811703000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/proc\/1997-125-02\/S0002-9939-97-03684-8\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,2]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1997,2]]}},"alternative-id":["S0002-9939-97-03684-8"],"URL":"https:\/\/doi.org\/10.1090\/s0002-9939-97-03684-8","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6826","0002-9939"],"issn-type":[{"value":"1088-6826","type":"electronic"},{"value":"0002-9939","type":"print"}],"subject":[],"published":{"date-parts":[[1997,2]]}}}