@UNPUBLISHED{publication1, title = "Gevrey well posedness of Goursat-Darboux problems and asymptotic solutions", author = "{MARQUES, Jorge} and {CARVALHO E SILVA, Jaime}", year = "2017-11-20", abstract = "We consider the generalized Goursat-Darboux problem for a third order linear PDE with real constant coefficients. Our purpose is to find necessary conditions for the problem to be well-posed in the Gevrey classes. Since this problem can be reduced to the Cauchy problem using permutations of independent variables, we solve it for a ODE with complex coefficients and two unknown initial data. In order to prove our results, we first construct an explicit solution of a family of problems with initial data depending on a parameter \η \> 0 and then we obtain an asymptotic representation of a solution as \η tends to infinity. ", url = "http://www.mat.uc.pt/preprints/eng\_2017.html", note = "" }