Global existence for a forced dispersive dissipative equation via the I-method

Bassam Kojok

doi:10.3934/cpaa.2009.8.1401

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2009, Volume 8, Issue 4: 1401-1419. Doi: 10.3934/cpaa.2009.8.1401

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Global existence for a forced dispersive dissipative equation via the I-method

Bassam Kojok^1,

1.
Laboratoire Analyse, Géométrie et Applications, Institut Galilée, Université Paris-Nord, 93430 Villetaneuse

Received: June 30, 2008

Revised: October 31, 2008

Published: June 2009

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Abstract

In this paper, we first investigate the Korteweg-de Vries-Burgers (KdV-Burgers) equation with low regularity external force $f$, where $f$ is a space-time function. We show that we can adapt the I-method to study the global well-posedness of our problem on a Sobolev space of negative index when a low regularity space-time external force occurs.

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Mathematics Subject Classification: Primary: 35Q53, 35B30, 42B35, 76B03, 76B15.

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