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On the Levi condition for Goursat problem

open access: yesKyoto Journal of Mathematics, 1987
The author treats the following differential operator \[ (1)\quad P(D_ t,D_ x,D_ y)=\sum^{m}_{j=\ell}C_ j(D_ x,D_ y)D_ t^{m- j}=P_ m+\sum^{m}_{k=1}P_{m-k}, \] where \(C_ j(\zeta,\eta)\) is a polynomial with constant coefficients of order \(\leq j\), and \(P_ j\) is a homogeneous part of degree j of P. Let \[ P_ m(\tau,\zeta,\eta)=\prod^{n'}_{j=1}(\zeta
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Adomian Decomposition Method for Solving Goursat's Problems

open access: yesApplied Mathematics, 2011
In this paper, Goursat’s problems for: linear and nonlinear hyperbolic equations of second-order, systems of nonlinear hyperbolic equations and fourth-order linear hyperbolic equations in which the attached conditions are given on the characteristics curves are transformed in such a manner that the Adomian decomposition method (ADM) can be applied ...
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Goursat rigid local systems of rank four [PDF]

open access: yes, 2018
Radchenko, D., Rodriguez Villegas, F.
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