Gevrey well posedness of Goursat-Darboux problems and asymptotic solutions (Preprint)

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Type: Preprint
National /International: International
Title: Gevrey well posedness of Goursat-Darboux problems and asymptotic solutions
Publication Date: 2017-11-20
Authors: - Jorge Marques
- Jaime Carvalho e Silva
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.
Institution: DMUC 17-47
Online version: http://www.mat.uc.pt...prints/eng_2017.html
Download: Not available
 
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