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| THE ABSTRACT CAUCHY PROBLEM AND A GENERALIZATION OF THE LUMER-PHILLIPS THEOREM |
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Citation： |
Li Yangrong.THE ABSTRACT CAUCHY PROBLEM AND A GENERALIZATION OF THE LUMER-PHILLIPS THEOREM[J].Chinese Annals of Mathematics B,1998,19(3):349~358 |
| Page view： 1201
Net amount： 890 |
Authors： |
Li Yangrong; |
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| Abstract： |
For injective, bounded operator $C$ on a Banach space $X$, the
author defines
the $C$-dissipative operator, and then gives Lumer-Phillips characterizations
of the generators of quasi-contractive $C$-semigroups, where a $C$-semigroup
$T(\cdot)$ is quasi-contractive if $\|T(t)x\|\le \|Cx\|$ for all $t\ge 0$ and
$x\in X$. This kind of generators guarantee that the associate abstract Cauchy
problem $u'(t,x)=Au(t,x)$ has a unique nonincreasing solution when the initial
data is in $C(D(A))$ (here $D(A)$ is the domain of $A$). Also,
the generators of quasi-isometric $C$-semigroups are characterized |
Keywords： |
Semigroups of operators, $C$-semigroups, Dissipative operators,
Abstract Cauchy problems |
Classification： |
47D03, 47D06 |
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