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Displaying similar documents to “Some results of Gevrey and analytic regularity for semilinear weakly hyperbolic equations of Oleinik type”

Propagation of analyticity of solutions to the Cauchy problem for Kirchhoff type equations

Kunihiko Kajitani (2000)

Journées équations aux dérivées partielles

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We shall give the local in time existence of the solutions in Gevrey classes to the Cauchy problem for Kirhhoff equations of p -laplacian type and investigate the propagation of analyticity of solutions for real analytic deta. When p = 2 , his equation as the global real analytic solution for the real analytic initial data.

Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators

Daniela Calvo (2006)

Bollettino dell'Unione Matematica Italiana

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We prove the well-posedness of the Cauchy Problem for first order weakly hyperbolic systems in the multi-anisotropic Gevrey classes, that generalize the standard Gevrey spaces. The result is obtained under the following hypotheses: the principal part is weakly hyperbolic with constant coefficients, the lower order terms satisfy some Levi-type conditions; and lastly the coefficients of the lower order terms belong to a suitable anisotropic Gevrey class. In the proof it is used the quasi-symmetrization...

Hyperbolicity of two by two systems with two independent variables

Tatsuo Nishitani (1998)

Journées équations aux dérivées partielles

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We study the simplest system of partial differential equations: that is, two equations of first order partial differential equation with two independent variables with real analytic coefficients. We describe a necessary and sufficient condition for the Cauchy problem to the system to be C infinity well posed. The condition will be expressed by inclusion relations of the Newton polygons of some scalar functions attached to the system. In particular, we can give a characterization of the...