An abstract nonlinear Cauchy-Kovalevska theorem
HTML articles powered by AMS MathViewer
- by François Trèves PDF
- Trans. Amer. Math. Soc. 150 (1970), 77-92 Request permission
Abstract:
A nonlinear version of Ovcyannikov’s theorem is proved. If $F(u,t)$ is an analytic function of $t$ real or complex and of $u$ varying in a scale of Banach spaces, valued in a scale of Banach spaces, the Cauchy problem ${u_t} = F(u,t),u(0) = {u_0}$, has a unique analytic solution. This is an abstract version of the Cauchy-Kovalevska theorem which can be applied to equations other than partial-differential, e.g. to certain differential-convolution or, more generally, differential-pseudodifferential equations.References
- L. V. Ovsjannikov, Singular operator in the scale of Banach spaces, Dokl. Akad. Nauk SSSR 163 (1965), 819–822 (Russian). MR 0190754 S. Steinberg and F. Treves, Pseudo-Fokker Planck equations and hyperdifferential operators, (to appear).
- François Trèves, On the theory of linear partial differential operators with analytic coefficients, Trans. Amer. Math. Soc. 137 (1969), 1–20. MR 247267, DOI 10.1090/S0002-9947-1969-0247267-8
- François Trèves, Ovcyannikov theorem and hyperdifferential operators, Notas de Matemática, No. 46, Instituto de Matemática Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1968. MR 0290202
Additional Information
- © Copyright 1970 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 150 (1970), 77-92
- MSC: Primary 35.03
- DOI: https://doi.org/10.1090/S0002-9947-1970-0274911-X
- MathSciNet review: 0274911