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Keywords
(1)
Semigroup of Linear Operators
Related Publications
(51)
Oneparameter Semigroups for Linear Evolution Equations
Analytic Semigroups and Optimal Regularity in Parabolic Problems
Existence and regularity for semilinear parabolic evolution equations
Semigroups of linear operators and applications
Geometric Theory of Nonlinear Parabolic Equations
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Semigroups of Linear Operators and Applications to Partial Differential Equations
Semigroups of Linear Operators and Applications to Partial Differential Equations,A. Pazy
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Semigroups of Linear Operators and Applications to Partial Differential Equations
(
Citations: 1650
)
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A. Pazy
Published in 1983.
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Citation Context
(343)
...Here we follow the same terminology as
17
...
Jingna Li
,
et al.
Wellposedness of fractional Ginzburg–Landau equation in Sobolev space...
...[
21
]). Moreover, note that (I +A) 1 = 1 R( 1 ;A) for > 0, and, by (D2), one gets (I +A) 1 (M) M...
...[
21
]) that the operatorA is an infinitesimal generator of a C0 semigroup SA with the propertykSA(t)kL(E;E) e 1t . One may also show that D(A) = H 1() \H 2 (), see [22], and that the semigroup generated byA is analytic, see [21]...
...[21]) that the operatorA is an infinitesimal generator of a C0 semigroup SA with the propertykSA(t)kL(E;E) e 1t . One may also show that D(A) = H 1() \H 2 (), see [22], and that the semigroup generated byA is analytic, see [
21
]...
...Since the resolvents ofA are compact operators, we infer, by [
21, Section 2.3
], that the semigroup is compact...
Aleksander Ćwiszewski
.
Positive periodic solutions of parabolic evolution problems: a transla...
...We need the following lemma: Lemma 2.5 [
19
] Assume that hypotheses (Al)(A3) hold, there exists evolution system U(t, s) , (0 ::; s ::; t ::; b) satisfies the following condition:...
Junhao Hu
,
et al.
Controllability of stochastic impulsive evolution differential inclusi...
...( X is not reflexive, because the second dual X∗∗ is not isomorphic to X.) As a consequence of the nonreflexivity of X, A∗0 is not densely defined on X∗, hence S∗ 0(t) is not strongly continuous on X ∗ = NBV([0, T],R2) by the HilleYosida theorem [
17, Theorem 5.2
]...
Róbert Szalai
,
et al.
Period Doubling Bifurcation and Center Manifold Reduction in a Timepe...
...Furthermore, by an evolution system U(t;s)0�s�t�T in B we mean a twoparameter family of bounded linear operators satisfying the usual strong continuity properties and composition laws (see for instance [
17
] or [19])...
...where n(x) stands for the outer unit normal vector at x. We do not specify further what such requirements might be, as there are many variants of them available in the existing literature (see for instance [
17
], [19], [21] and the references therein)...
PierreA. Vuillermot
.
A generalization of Chernoff's product formula for timedependent oper...
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Citations
(1650)
Wellposedness of fractional Ginzburg–Landau equation in Sobolev spaces
Jingna Li
,
Li Xia
Journal:
Applicable Analysis
, vol. aheadofp, no. aheadofp, pp. 111, 2012
The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds
(
Citations: 2
)
Peter E. Kloeden
,
Gabriel J. Lord
,
A. Neuenkirch
,
Tony Shardlow
Journal:
Journal of Computational and Applied Mathematics  J COMPUT APPL MATH
, vol. 235, no. 5, pp. 12451260, 2011
The existence and exponential stability of semilinear functional differential equations with random impulses under nonuniqueness
(
Citations: 1
)
A. Anguraj
,
Shujin Wu
,
A. Vinodkumar
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 74, no. 2, pp. 331342, 2011
Controllability of impulsive differential systems with nonlocal conditions
(
Citations: 1
)
Shaochun Ji
,
Gang Li
,
Min Wang
Journal:
Applied Mathematics and Computation  AMC
, vol. 217, no. 16, pp. 69816989, 2011
Synthesis of nanoporous metal oxides through the selfassembly of phloroglucinol–formaldehyde resol and triblock copolymer
(
Citations: 1
)
M. U. Anu Prathap
,
Rajendra Srivastava
Journal:
Journal of Colloid and Interface Science  J COLLOID INTERFACE SCI
, vol. 358, no. 2, pp. 399408, 2011