Persistence properties for a family of nonlinear partial differential equations

David Henry

doi:10.1016/j.na.2008.02.104

Persistence properties for a family of nonlinear partial differential equations

David Henry

Trinity College Dublin

Research output: Contribution to journal › Article › peer-review

Abstract

We examine the persistence of decay properties for a family of dispersive nonlinear partial differential equations. We show that certain decay properties of the initial data persist for as long as the solution exists. On the other hand, for a subset of the family certain decay rates are possible only for the trivial solution. For example, the only solution that remains with compact support for any further time is the trivial solution.

Original language	English
Pages (from-to)	1565-1573
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	70
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2008.02.104
Publication status	Published - 15 Feb 2009
Externally published	Yes

Keywords

b-equations
Compactly-supported solutions
Persistence of decay rates

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10.1016/j.na.2008.02.104

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AB - We examine the persistence of decay properties for a family of dispersive nonlinear partial differential equations. We show that certain decay properties of the initial data persist for as long as the solution exists. On the other hand, for a subset of the family certain decay rates are possible only for the trivial solution. For example, the only solution that remains with compact support for any further time is the trivial solution.

KW - b-equations

KW - Compactly-supported solutions

KW - Persistence of decay rates

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DO - 10.1016/j.na.2008.02.104

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JO - Nonlinear Analysis, Theory, Methods and Applications

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Persistence properties for a family of nonlinear partial differential equations

Abstract

Keywords

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