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951.
We consider a steady-state heat conduction problem P
α
with mixed boundary conditions for the Poisson equation depending on a positive parameter α , which represents the heat transfer coefficient on a portion Γ
1
of the boundary of a given bounded domain in R
n
. We formulate distributed optimal control problems over the internal energy g for each α . We prove that the optimal control g_ op
α
and its corresponding system u_ g_ op
α
α and adjoint p_ g_ op
α
α states for each α are strongly convergent to g
op
, u_ g
op
and p _ g
op
, respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control,
and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation
with a different boundary condition on the portion Γ
1
. We use the fixed point and elliptic variational inequality theories. 相似文献
952.
Hyperbolicity of an autonomous rest point is characterised by its linearization not having eigenvalues on the imaginary axis. More generally, hyperbolicity of any solution which exists for all times can be defined by means of Lyapunov exponents or exponential dichotomies. We go one step further and introduce a meaningful notion of hyperbolicity for linear systems which are defined for finite time only, i.e. on a compact time interval. Hyperbolicity now describes the transient dynamics on that interval. In this framework, we provide a definition of finite-time spectrum, study its relations with classical concepts, and prove an analogue of the Sacker-Sell spectral theorem: For a d-dimensional system the spectrum is non-empty and consists of at most d disjoint (and often compact) intervals. An example illustrates that the corresponding spectral manifolds may not be unique, which in turn leads to several challenging questions. 相似文献
953.
In this paper, we consider the long-time behavior of small solutions of the Cauchy problem for a generalized Boussinesq equation. A scattering operator and the nonlinear scattering for small amplitude solutions of the Boussinesq equation are established under certain hypotheses. 相似文献
954.
Victor G. Zvyagin Dmitry A. Vorotnikov 《Journal of Fixed Point Theory and Applications》2008,3(1):23-49
We describe a new approach to the study of initial-boundary value problems for evolutionary equations of hydrodynamics, which
is based on approximation of the problems and subsequent application of topological degree theory for investigation of weak
solvability for approximating problems. Use of this method turned out to be especially effective in problems of non- Newtonian
hydrodynamics. We demonstrate its application to the study of weak solvability and attractors of the initial-boundary value
problem for the Oldroyd model with regularized objective Jaumann derivative. 相似文献
955.
Terence Parsons 《Logica Universalis》2008,2(1):3-11
The truth conditions that Aristotle attributes to the propositions making up the traditional square of opposition have as
a consequence that a particular affirmative proposition such as ‘Some A is not B’ is true if there are no Bs. Although a different
convention than the modern one, this assumption remained part of centuries of work in logic that was coherent and logically
fruitful.
相似文献
956.
John E. Hutchinson Yoshihiro Tonegawa 《Calculus of Variations and Partial Differential Equations》2000,10(1):49-84
We study the general asymptotic behavior of critical points, including those of non-minimal energy type, of the functional
for the van der Waals-Cahn-Hilliard theory of phase transitions. We prove that the interface is close to a hypersurface with
mean curvature zero when no Lagrange multiplier is present, and with locally constant mean curvature in general. The energy
density of the limiting measure has integer multiplicity almost everywhere modulo division by a surface energy constant.
Received March 16, 1999 / Accepted June 11, 1999 相似文献
957.
Paschalis Karageorgis 《Journal of Differential Equations》2005,219(2):259-305
We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of small-amplitude solutions is driven by the nonlinear term. If the potential induces growth in the linearized problem, however, solutions that start out small may blow-up in finite time. 相似文献
958.
959.
It was proved implicitly by Ingleton and Main and explicitly by Lindström that if three lines in the algebraic matroid consisting of all elements of an algebraically closed field are not coplanar, but any two of them are, then they pass through one point. This theorem is extended to a more general result about the intersection of subspaces in full algebraic matroids. This result is used to show that the minimax theorem for matroid matching, proved for linear matroids by Lovász, remains valid for algebraic matroids. 相似文献
960.
Temperature measurements alone, and also simultaneous CO2 concentration and temperature measurements, have been performed inside a fired IC engine. To tackle the two main problems encounted when making measurements in an engine (i.e., cycle-to-cycle variations and beam steering by density gradients), the shot-by-shot referencing technique and the in situ referencing technique using N2 to determine [CO2] were used. The temperature is deduced from the broadband N2 CARS signal and narrow band detection is used for CO2. A representative example of temperature measurements is given which shows a correlation between temperature and knocking intensity in the burnt gas of a knocking engine. The first simultaneous determinations of temperature and [CO2] are also reported; so far these are reliable only during the compression stoke. 相似文献