Existence and decay of solutions of an abstract second order nonlinear problem

In this paper we consider the following nonlinear evolution problem with damping: (∗) | u ″ ( t ) + A u ( t ) + B α u ′ ( t ) = 0 , t > 0 , u ( 0 ) = u 0 , u ′ ( 0 ) = u 1 where A is a monotone nonlinear operator, B α a linear operator and α a real number with 0 < α ⩽ 1 . We study the global e...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-10, Vol.358 (2), p.445-456
Main Authors: Maia, S.A., Milla Miranda, M.
Format: Article
Language:English
Subjects:
Convex functional
Exact sciences and technology
Mathematical analysis
Mathematics
Monotone operator
Operator theory
Sciences and techniques of general use
Second order nonlinear problem
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Summary:In this paper we consider the following nonlinear evolution problem with damping: (∗) | u ″ ( t ) + A u ( t ) + B α u ′ ( t ) = 0 , t > 0 , u ( 0 ) = u 0 , u ′ ( 0 ) = u 1 where A is a monotone nonlinear operator, B α a linear operator and α a real number with 0 < α ⩽ 1 . We study the global existence and decay of solutions of problem (∗).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.02.047