Abstract
We consider a class of linear systems whose principal symbol satisfies a certain condition of semi-hyperbolicity, and we prove the local surjectivity in suitable Gevrey spaces.
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References
M.D. BronshteinSmoothness of polynomials depending on parametersSib. Mat. Zh.20(1979), 493–501.
M.D. BronshteinThe Cauchy problem for hyperbolic operators with multiple variable characteristicsTrudy Moskow Mat. Obsc.41(1980), 83–99; Trans. Moscow Math. Soc.1(1982), 87–103.
T. Gramchev and L. RodinoGevrey solvability for semilinear partial differential equations with multiple characteristicsBoll. Un. Mat. It.2-B(1999), 65–120.
T. GramchevOn the critical index of Gevrey Solvability for some linear partial differential equationsAnn. Univ. Ferrara Sez. Sci. Mat., Suppl.14(1999), 139–153.
K. KajitaniLocal solution of the Cauchy problem for hyperbolic systems in Gervrey classesHokkaido Math.J. 12(1983), 434–460.
P.R. PopivanovLocal solvability of some classes of linear differential operators with multiple characteristicsAnn. Univ. Ferrara Sez. Sci. Mat., Suppl.24(1999), 263–274.
S. SpagnoloLocal and semi-global solvability for systems of non-principal typeComm. Part. Diff. Equat.25(2000), 1115–1141.
S. WakabayashiRemarks on hyperbolic polynomialsTsukuba J. Math. 10 (1986), 17–28.
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© 2003 Springer Science+Business Media New York
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Kajitani, K., Spagnolo, S. (2003). Strong Gevrey Solvability for a System of Linear Partial Differential Equations. In: Kajitani, K., Vaillant, J. (eds) Partial Differential Equations and Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 52. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0011-6_11
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DOI: https://doi.org/10.1007/978-1-4612-0011-6_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6572-6
Online ISBN: 978-1-4612-0011-6
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