Results 21 to 30 of about 300 (51)
Abstract and Applied Analysis, Volume 2004, Issue 12, Page 1007-1018, 2004., 2004 In the class of scalar type spectral operators in a complex Banach space, a characterization of the generators of analytic C0‐semigroups in terms of the analytic vectors of the operators is found.
Marat V. Markin
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Lyapunov theorems for Banach spaces
, 1993 We present a spectral mapping theorem for semigroups on any Banach space $E$. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for $E$-valued functions.
Latushkin, Yuri +1 more
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Analyticity and Riesz basis property of semigroups associated to damped vibrations [PDF]
, 2007 Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract Hilbert space are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping.
Jacob, Birgit +2 more
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An inverse problem for a second‐order differential equation in a Banach space
Abstract and Applied Analysis, Volume 2004, Issue 12, Page 997-1005, 2004., 2004 We consider the problem of determining the unknown term in the right‐hand side of a second‐order differential equation with unbounded operator generating a cosine operator function from the overspecified boundary data. We obtain necessary and sufficient conditions of the unique solvability of this problem in terms of location of the spectrum of the ...
Y. Eidelman
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Abstract and Applied Analysis, Volume 2004, Issue 10, Page 881-896, 2004., 2004 Let u be a given bounded uniformly continuous mild solution of a higher‐order abstract functional differential equation of delay or advance type. We give a so‐called Massera‐type criterion for the existence of a mild solution, which is a “spectral component” of u with spectrum similar to the one of the forcing term f.
Nguyen Van Minh, Ha Binh Minh
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Asymptotic parabolicity for strongly damped wave equations
, 2013 For $S$ a positive selfadjoint operator on a Hilbert space, \[ \frac{d^2u}{dt}(t) + 2 F(S)\frac{du}{dt}(t) + S^2u(t)=0 \] describes a class of wave equations with strong friction or damping if $F$ is a positive Borel function.
Fragnelli, Genni +3 more
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On the Lw2‐boundedness of solutions for products of quasi‐integro differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 10, Page 639-659, 2003., 2003 Given a general quasi‐differential expressions τ1, τ2, …, τn each of order n with complex coefficients and their formal adjoints are τ1+,τ2+,…,τn+ on [0, b), respectively, we show under suitable conditions on the function F that all solutions of the product of quasi‐integrodifferential equation [∏j=1nτj]y=wF(t,y,∫0tg(t,s,y,y′,…,y(n2−1)(s))ds) on [0, b),
Sobhy El-Sayed Ibrahim
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Almost periodic solutions of periodic linear partial functional differential equations
, 2018 We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$.
Luong, Vu Trong, Van Minh, Nguyen
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Linear neutral partial differential equations: a semigroup approach
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 23, Page 1433-1445, 2003., 2003 We study linear neutral PDEs of the form (∂/∂t)Fut = BFut + Φut, t ≥ 0; u0(t) = φ(t), t ≤ 0, where the function u(⋅) takes values in a Banach space X. Under appropriate conditions on the difference operator F and the delay operator Φ, we construct a C0‐semigroup on C0(ℝ−, X) yielding the solutions of the equation.
Rainer Nagel, Nguyen Thieu Huy
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