On the Cauchy problem for some non-Kowalewskian equations in \(\mathcal{D}^{[\sigma]}_{L^ 2}\)

DOI10.1007/BF01758984zbMath0879.35166MaRDI QIDQ678154

Juan-Miguel Gracia

Publication date: 1 June 1997

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

Cauchy problemwell-posednessGevrey classes

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) General theory of partial differential operators (47F05) Initial value problems for PDEs with pseudodifferential operators (35S10)

Cites Work

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• Some remarks on the Cauchy problem
• Some remarks on my paper On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots
• Some remarks on the Cauchy problem for Schrödinger type equations
• Fourier integral operators in Gevrey class on \({\mathbb{R}}^ n\) and the fundamental solution for a hyperbolic operator
• Fundamental solutions and eigenfunction expansions for Schrödinger operators. I: Fundamental solutions
• On some Schrödinger type equations
• Fundamental solution of the Cauchy problem for a Schrödinger pseudo- differential operator
• Remarks on pseudo-differential operators
• Sufficient condition on H_∞well poeesne for schrodinger type equations
• A necessary condition or the well-posedness of the Cauchy problem or a certain class of evolution equations
• ON THE CAUCHY PROBLEM FOR SOME PSEUDO-DIFFERENTIAL EQUATIONS OF SCHRÖDINGER TYPE
• The Cauchy problem for Schrödinger type equations with variable coefficients

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