The Cauchy problem and Hadamard's example

Jan Persson

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Counterexamples to Hölmgren's uniqueness for analytic non linear Cauchy problem.

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

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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.

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Angus E. Taylor (1937)

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Global solvability for the degenerate Kirchhoff equation

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Analytic continuation for some classes of separately analytic functions of real variables

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For functions that are separately solutions of an elliptic homogeneous PDE with constant coefficients, we prove an analogue of Siciak's theorem for separately holomorphic functions.

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On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments

Antoni Augustynowicz (1999)

Annales Polonici Mathematici

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We prove an existence theorem of Cauchy-Kovalevskaya type for the equation $D_{t} u (t, z) = f (t, z, u (α^{(0)} (t, z)), D_{z} u (α^{(1)} (t, z)), . . ., D_{z}^{k} u (α^{(k)} (t, z)))$ where f is a polynomial with respect to the last k variables.