Gevrey well posedness of the generalized Goursat-Darboux problem for a linear PDE (Preprint)

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Type: Preprint
National /International: International
Title: Gevrey well posedness of the generalized Goursat-Darboux problem for a linear PDE
Publication Date: 2018-04-19
Authors: - Jorge Marques
- Jaime Carvalho e Silva
Abstract: We consider the generalized Goursat-Darboux problem for a third order linear PDE with real coefficients. Our purpose is to find necessary conditions for the problem to be well-posed in the Gevrey classes Γs with s > 1. It is proved that there exists some critical index s 0 such that if the Goursat-Darboux problem is well posed in Γs for s > s0 then some conditions should be imposed on the coefficients of the derivatives with respect to one of the variables. In order to prove our results, we first construct an explicit solution of a family of problems with data depending on a parameter η > 0 and then we obtain an asymptotic representation of a solution as η tends to infinity.
Institution: DMUC 18-13
Online version: http://www.mat.uc.pt...prints/eng_2018.html
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