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1.
In this paper, we prove the invariance of Stepanov-like pseudo-almost periodic functions under bounded linear operators. Furthermore, we obtain existence and uniqueness theorems of pseudo-almost periodic mild solutions to evolution equations u′(t)=A(t)u(t)+h(t) and on , assuming that A(t) satisfy “Acquistapace–Terreni” conditions, that the evolution family generated by A(t) has exponential dichotomy, that R(λ0,A()) is almost periodic, that B,C(t,s)t≥s are bounded linear operators, that f is Lipschitz with respect to the second argument uniformly in the first argument and that h, f, F are Stepanov-like pseudo-almost periodic for p>1 and continuous. To illustrate our abstract result, a concrete example is given. 相似文献
2.
Peter Lesky 《Mathematical Methods in the Applied Sciences》1992,15(7):453-468
We study the initial-boundary value problem for ?t2u(t,x)+A(t)u(t,x)+B(t)?tu(t,x)=f(t,x) on [0,T]×Ω(Ω??n) with a homogeneous Dirichlet boundary condition; here A(t) denotes a family of uniformly strongly elliptic operators of order 2m, B(t) denotes a family of spatial differential operators of order less than or equal to m, and u is a scalar function. We prove the existence of a unique strong solution u. Furthermore, an energy estimate for u is given. 相似文献
3.
It is shown that large classes of control systems, which include certain systems of the typex+A(t)x=B(t)u, can be handled in such a way that the control functionsu(t) are actually associated with responsesx(t) that belong to known families of functions. In particular, it is possible, for a variety of perturbationsB(t)u and operatorsA(t) with convex domains, to have responses that are line segments joining the origin to the reachable states.The present approach establishes the fact that a vast number of results from functional analysis concerning ranges of operators can be effectively applied to the general theory of control. It is also rather significant that the present theory does not necessarily require the solvability of the associated Cauchy problem.The operatorsB(t)u do not have to be invertible inu. However, it is shown that continuous controlsu(t) can be obtained for a variety of problems whenB
–1(t)u exists and is continuous int. 相似文献
4.
We study the asymptotic behavior for solutions to nonlocal diffusion models of the form u
t
= J * u – u in the whole with an initial condition u(x, 0) = u
0(x). Under suitable hypotheses on J (involving its Fourier transform) and u
0, it is proved an expansion of the form
, where K
t
is the regular part of the fundamental solution and the exponent A depends on J, q, k and the dimension d.
Moreover, we can obtain bounds for the difference between the terms in this expansion and the corresponding ones for the expansion
of the evolution given by fractional powers of the Laplacian, .
相似文献
5.
Let E be a separable Banach space ordered by a reproducing cone with empty interior. We prove the existence of operator functions A : [0, ) P (P the cone of monotone increasing linear operators) and of initial values x0 such that the solution of x (t) = A(t) x(t), x(0) = x0, is dense in E.Received: 27 February 2004 相似文献
6.
Luciana Angiuli Michele MirandaJr Diego Pallara Fabio Paronetto 《Annali di Matematica Pura ed Applicata》2009,188(2):297-331
Given a uniformly elliptic second order operator on a possibly unbounded domain , let (T(t))
t≥0 be the semigroup generated by in L
1(Ω), under homogeneous co-normal boundary conditions on ∂Ω. We show that the limit as t → 0 of the L
1-norm of the spatial gradient D
x
T(t)u
0 tends to the total variation of the initial datum u
0, and in particular is finite if and only if u
0 belongs to BV(Ω). This result is true also for weighted BV spaces. A further characterization of BV functions in terms of the short-time behaviour of (T(t))
t≥0 is also given.
相似文献
7.
In a Banach space E, we consider the inverse problem du(t)/dt = Au(t) + (t)p , u(0) = u
0, u(T) = u1, with an unknown function u(t) and an element p E. The operator A is assumed linear and closed. In this paper, we establish minimal constraints on the function C([0, T]) for which the uniqueness of the solution of the inverse problem is completely described in terms of the eigenvalues of the operator A.Translated from Matematicheskie Zametki, vol. 77, no. 2, 2005, pp. 273–290.Original Russian Text Copyright © 2005 by I. V. Tikhonov, Yu. S. Éidelman.This revised version was published online in April 2005 with a corrected issue number. 相似文献
8.
Grgoire Nadin 《Journal de Mathématiques Pures et Appliquées》2009,92(3):232-262
This paper is concerned with the existence of pulsating traveling fronts for the equation:(1)
∂tu−(A(t,x)u)+q(t,x)u=f(t,x,u),