Higher-order degenerate Cauchy problems in locally convex spaces

We establish a criterion for the C-well-posedness of higher order degenerate Cauchy problems (DCP n ) in a sequentially complete locally convex space by introducing a C-propagation family { P( t)} t≥0 for (DCP n ). This result is applied then to a class of (DCP 2) whose coefficient operators are dif...

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Bibliographic Details
Published in:Mathematical and computer modelling 2005-03, Vol.41 (6), p.837-847
Main Authors: Liang, Jin, Xiao, Ti-Jun
Format: Article
Language:English
Subjects:
C-propagation family
C-well-posedness
Degenerate differential equations
Differential operators
Fourier multipliers
Higher-order Cauchy problems
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Summary:We establish a criterion for the C-well-posedness of higher order degenerate Cauchy problems (DCP n ) in a sequentially complete locally convex space by introducing a C-propagation family { P( t)} t≥0 for (DCP n ). This result is applied then to a class of (DCP 2) whose coefficient operators are differential operators on various function spaces with Fréchet topologies and two C-well-posedness Theorems are obtained.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2003.11.010