Differential and Integral Equations

On the local ill-posedness of the generalized $p$-Gardner equation

Gilberto Arenas-Díaz and José R. Quintero

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In this paper, we adapt and extend B. Birnir, G. Ponce, and N. Svanstedt result related with local ill-posedness for the Cauchy problem to the mKdV equation in [5] to the generalized $p$-Gardner equation. We prove that the Cauchy problem for the generalized $2$-Gardner equation is ill-posed in the Sobolev space $H^s(\mathbb{R})$ for $s < -\frac12$.

Article information

Differential Integral Equations, Volume 27, Number 11/12 (2014), 1025-1036.

First available in Project Euclid: 18 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q51: Soliton-like equations [See also 37K40] 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 37K40: Soliton theory, asymptotic behavior of solutions


Quintero, José R.; Arenas-Díaz, Gilberto. On the local ill-posedness of the generalized $p$-Gardner equation. Differential Integral Equations 27 (2014), no. 11/12, 1025--1036. https://projecteuclid.org/euclid.die/1408366783

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