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Xiao T-J., Liang J. — The Cauchy Problem for Higher-Order Abstract Differential Equations
Xiao T-J., Liang J. — The Cauchy Problem for Higher-Order Abstract Differential Equations

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Название: The Cauchy Problem for Higher-Order Abstract Differential Equations

Авторы: Xiao T-J., Liang J.


This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2006

Количество страниц: 301

Добавлена в каталог: 11.12.2009

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Предметный указатель
$(ACP_{2})$      2.5
$(ACP_{n})$      Preface
$(ACP_{n})$, analytically solvable in $\Sigma_{\theta}$      4.1
$(ACP_{n})$, entire solution      4.4
$(ACP_{n})$, propagator      2.1
$(ACP_{n})$, solution      2.1
$(ACP_{n})$, solvability      2.3
$(ACP_{n})$, strong C-propagation family      3.5
$(ACP_{n})$, strongly C-wellposed      3.5
$(ACP_{n})$, strongly wellposed      2.1
$(ACP_{n})$, wellposed      2.1
$(ACP_{n})_{[B_{n-1}, ... ,B_{0}]}$      2.4
$(ACP_{n})_{[B_{n-1}, ... ,B_{0}]}$, analytically solvable      4.2
$(ACP_{n})_{[B_{n-1}, ... ,B_{0}]}$, analytically wellposed      4.1
$(ACP_{n})_{[B_{n-1}, ... ,B_{0}]}$, propagator      2.4
$(ACP_{n})_{[B_{n-1}, ... ,B_{0}]}$, solution      2.4
$(ACP_{n})_{[B_{n-1}, ... ,B_{0}]}$, strongly wellposed      2.4
$(E^{B}_{m}, \|u\|^{B}_{m})$      3.3
$(^{r}_{j})$      1.5
$A_{K}$      Preface
$C(R^{+},E)$      Preface
$C^{k}(R^{+},E)$      Preface
$C^{\infty}(R^{+},E)$      Preface
$L^{p}_{l}(R^{n})$      1.5
$N^{l}_{0}$      1.5
$N_{0}$      Preface
$N_{e}$      3.5
$P_{\lambda}$      Preface 2.5
$R^{+}$      Preface
$r_{p}$      1.5
$R_{\lambda}$      Preface 2.5
$S^{(j)}_{k}(t)$      2.1
$T_{l}<u>$      1.5
$UC_{b}(R^{n})$      3.5
$W^{a,p}_{l}(R^{n})$      1.5
$[\mathcal{D}(A)]$      3.4
$\ast m$      1.1
$\Delta$      1.6 3.5
$\delta_{kl}$      2.1
$\gamma$      Preface 1.1
$\mathbf{P}_{\lambda}$      7.2
$\mathcal{A}_{n}$      4.2
$\mathcal{A}_{n}(\theta)$      4.2
$\mathcal{A}_{n}(\theta)_{[B_{n-1}, ... ,B_{0}]}$      4.2
$\mathcal{B}_{\Gamma}(E)$      Preface
$\mathcal{D}(A)$      Preface
$\mathcal{F}f$, $\hat{f}$      1.5
$\mathcal{F}L^{1}$      1.5
$\mathcal{F}^{-1}f$      1.5
$\mathcal{H}_{a}$      5.1
$\mathcal{L}[h(t)](\lambda)$      1.1
$\mathcal{M}_{p}$      1.5
$\mathcal{N}(A)$      Preface
$\mathcal{P}_{\lambda}$      7.1
$\mathcal{S}(R^{n})$      1.5
$\omega_{0}$, $\omega_{0}(A_{0}, ... ,A_{n-1})$      5.1
$\rho(A)$      Preface
$\rho(A_{0}, ... ,A_{n-1})$      3.5
$\rho_{0}(A_{0}, ... ,A_{n-1})$      4.1
$\rho_{C}(A)$      1.3
$\rho_{C}(A_{0}, ... ,A_{n-1})$      3.5
$\sigma(A)$      Preface
$\Sigma_{b}$      6.1
$\sigma_{p}(A)$      Preface
$\Sigma_{\theta}$      3.6
$\sqrt{z}$      3.5
$\theta^{\pm}_{\infty}(B)$      4.2
$\Upsilon_{\phi}(\theta,r)$      4.4
$\|\cdot\|_{\Gamma}$      Preface
<b>      3.2
A*      Preface
Almost periodic (a.p.)      7.1 7.2
Almost periodic (a.p.), weakly almost periodic (w.a.p.)      7.1
Analytic semigroup of angle $\theta$      A2
Analytically wellposed in $\Sigma_{\theta}$      4.1
Bernstein's theorem      1.5
C      Preface
C-regularized cosine function      1.4
C-regularized semigroup      1.3
Complete $(ACP_{2})$      Summary in Chapt.2
Differentiable semigroup      A2
Dissipative operator      A2
E*      1.1
Elliptic      1.5
Elliptic, strongly elliptic      3.5
Equicontinuous      1.1
Equicontinuous, $\Gamma(M)$-      1.1
Equicontinuous, $\Gamma(M_{p})$-      1.1
Exponential growth bound      5.1
Exponential growth bound, type      5.3
Exponentially stable      5.1
Fourier multiplier      1.5
Fourier transform      1.5
Hille — Yosida — Feller — Miyadera — Phillips type theorem      2.2
Incomplete $(ACP_{2})$      Summary in Chapt.2
L(E)      Preface
L(E, X)      Preface
Laplace transform      1.1
Laplace transform, determining function      1.1
Laplace transform, uniqueness theorem      1.1
LT - E      1.1
LT - L(E)      1.1
Lumer — Phillips theorem      A2
Moment inequality      4.1
N      Preface
Nonnegative operator      3.6
Nonnegative operator, fractional power      A1
Norm continuous      6.2
Parabolic      4.2
Phillips perturbation theorem      A2
R      Preface
R($\lambda$; A)      Preface
r-times integrated cosine function      1.4
r-times integrated semigroup      1.4
r-times integrated, C-regularized cosine function      1.4
r-times integrated, C-regularized cosine function, generator      1.4
r-times integrated, C-regularized cosine function, subgenerator      1.4
r-times integrated, C-regularized semigroup      1.3
r-times integrated, C-regularized semigroup, generator      1.3
r-times integrated, C-regularized semigroup, subgenerator      1.3
SCLCS      1.1
Strongly continuous $H(\cdot):R^{+}\rightarrow L(E)$      1.1
Strongly continuous cosine function      A2
Strongly continuous cosine function, generator      A2
Strongly continuous group      A2
Strongly continuous group, generator      A2
Strongly continuous semigroup      A2
Strongly continuous semigroup, generator      A2
Strongly continuous semigroup, strongly continuous semigroups of contractions      A2
T<u>      1.5 3.5
[b]      Preface
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