<Reference List> | |
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 |