Article

Existence of solutions in the alpha-norm for partial differential equations of neutral type with finite delay

Electronic Journal of Differential Equations 01/2010; DOI:http://www.doaj.org/doaj?func=openurl&genre=article&issn=10726691&date=2010&volume=2010&issue=157,&spage=1
Source: DOAJ

ABSTRACT In this work, we prove results on the local existence of mild solution and global continuation in the alpha-norm for some class of partial neutral differential equations. We suppose that the linear part generates a compact analytic semigroup. The nonlinear part is just assumed to be continuous. We use the compactness method, to show the main result of this work.

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Keywords

compact analytic semigroup
 
compactness method
 
global continuation
 
local existence
 
nonlinear part
 
partial neutral differential equations