共查询到20条相似文献,搜索用时 31 毫秒
1.
Jan A. van Casteren 《Journal of Evolution Equations》2011,11(2):457-476
Let
(tj)j ? \mathbbN{\left(\tau_j\right)_{j\in\mathbb{N}}} be a sequence of strictly positive real numbers, and let A be the generator of a bounded analytic semigroup in a Banach space X. Put
An=?j=1n(I+\frac12 tjA) (I-\frac12 tjA)-1{A_n=\prod_{j=1}^n\left(I+\frac{1}{2} \tau_jA\right) \left(I-\frac{1}{2} \tau_jA\right)^{-1}}, and let x ? X{x\in X}. Define the sequence
(xn)n ? \mathbbN ì X{\left(x_n\right)_{n\in\mathbb{N}}\subset X} by the Crank–Nicolson scheme: x
n
= A
n
x. In this paper, it is proved that the Crank–Nicolson scheme is stable in the sense that
supn ? \mathbbN||Anx|| < ¥{\sup_{n\in\mathbb{N}}\left\Vert A_nx\right\Vert<\infty}. Some convergence results are also given. 相似文献
2.
Markus Haase 《Integral Equations and Operator Theory》2006,56(2):197-228
We generalize a Hilbert space result by Auscher, McIntosh and Nahmod to arbitrary Banach spaces X and to not densely defined injective sectorial operators A. A convenient tool proves to be a certain universal extrapolation space associated with A. We characterize the real interpolation space
( X,D( Aa ) ?R( Aa ) )q,p{\left( {X,\mathcal{D}{\left( {A^{\alpha } } \right)} \cap \mathcal{R}{\left( {A^{\alpha } } \right)}} \right)}_{{\theta ,p}}
as
{ x ? X|t - q\textRea y1 ( tA )x, t - q\textRea y2 ( tA )x ? L*p ( ( 0,¥ );X ) } {\left\{ {x\, \in \,X|t^{{ - \theta {\text{Re}}\alpha }} \psi _{1} {\left( {tA} \right)}x,\,t^{{ - \theta {\text{Re}}\alpha }} \psi _{2} {\left( {tA} \right)}x \in L_{*}^{p} {\left( {{\left( {0,\infty } \right)};X} \right)}} \right\}} 相似文献
3.
Shangquan Bu 《Integral Equations and Operator Theory》2011,71(2):259-274
We study the well-posedness of the fractional differential equations with infinite delay (P
2): Da u(t)=Au(t)+òt-¥a(t-s)Au(s)ds + f(t), (0 £ t £ 2p){D^\alpha u(t)=Au(t)+\int^{t}_{-\infty}a(t-s)Au(s)ds + f(t), (0\leq t \leq2\pi)}, where A is a closed operator in a Banach space ${X, \alpha > 0, a\in {L}^1(\mathbb{R}_+)}${X, \alpha > 0, a\in {L}^1(\mathbb{R}_+)} and f is an X-valued function. Under suitable assumptions on the parameter α and the Laplace transform of a, we completely characterize the well-posedness of (P
2) on Lebesgue-Bochner spaces
Lp(\mathbbT, X){L^p(\mathbb{T}, X)} and periodic Besov spaces
B p,qs(\mathbbT, X){{B} _{p,q}^s(\mathbb{T}, X)} . 相似文献
4.
Daniela Roşu 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(4):479-496
In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, ${\mathcal{K}}
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