Differential and Integral Equations

Optimal well-posedness of the Cauchy problem for evolution equations with $C^N$ coefficients

Massimo Cicognani and Ferruccio Colombini

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Abstract

We deal with the Cauchy problem for a $2$-evolution operator of Schrödinger type with $C^N$ coefficients in the time variable, $N>2$. We find the Levi conditions for well-posedness in Gevrey classes of index $1/2 + N/4$, which is the best possible, as we show by means of counterexamples.

Article information

Source
Differential Integral Equations, Volume 17, Number 9-10 (2004), 1079-1092.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060314

Mathematical Reviews number (MathSciNet)
MR2082460

Zentralblatt MATH identifier
1150.35351

Subjects
Primary: 35G10: Initial value problems for linear higher-order equations
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Citation

Cicognani, Massimo; Colombini, Ferruccio. Optimal well-posedness of the Cauchy problem for evolution equations with $C^N$ coefficients. Differential Integral Equations 17 (2004), no. 9-10, 1079--1092. https://projecteuclid.org/euclid.die/1356060314


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