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## Classical Solution (classical + solution)
## Selected Abstracts## Optimality for the linear quadratic non-Gaussian problem via the asymmetric Kalman filter INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 1 2004Rosario RomeraAbstract In the linear non-Gaussian case, the classical solution of the linear quadratic Gaussian (LQG) control problem is known to provide the best solution in the class of linear transformations of the plant output if optimality refers to classical least-squares minimization criteria. In this paper, the adaptive linear quadratic control problem is solved with optimality based on asymmetric least-squares approach, which includes least-squares criteria as a special case. Our main result gives explicit solutions for this optimal quadratic control problem for partially observable dynamic linear systems with asymmetric observation errors. The main difficulty is to find the optimal state estimate. For this purpose, an asymmetric version of the Kalman filter based on asymmetric least-squares estimation is used. We illustrate the applicability of our approach with numerical results. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Robustness analysis of flexible structures: practical algorithms INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2003Gilles FerreresAbstract When analysing the robustness properties of a flexible system, the classical solution, which consists of computing lower and upper bounds of the structured singular value (s.s.v.) at each point of a frequency gridding, appears unreliable. This paper describes two algorithms, based on the same technical result: the first one directly computes an upper bound of the maximal s.s.v. over a frequency interval, while the second one eliminates frequency intervals, inside which the s.s.v. is guaranteed to be below a given value. Various strategies are then proposed, which combine these two techniques, and also integrate methods for computing a lower bound of the s.s.v. The computational efficiency of the scheme is illustrated on a real-world application, namely a telescope mock-up which is significant of a high order flexible system. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Point-wise decay estimate for the global classical solutions to quasilinear hyperbolic systems MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2009Yi ZhouAbstract In this paper, we first consider the Cauchy problem for quasilinear strictly hyperbolic systems with weak linear degeneracy. The existence of global classical solutions for small and decay initial data was established in (Commun. Partial Differential Equations 1994; 19:1263,1317; Nonlinear Anal. 1997; 28:1299,1322; Chin. Ann. Math. 2004; 25B:37,56). We give a new, very simple proof of this result and also give a sharp point-wise decay estimate of the solution. Then, we consider the mixed initial-boundary-value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in the first quadrant. Under the assumption that the positive eigenvalues are weakly linearly degenerate, the global existence of classical solution with small and decay initial and boundary data was established in (Discrete Continuous Dynamical Systems 2005; 12(1):59,78; Zhou and Yang, in press). We also give a simple proof of this result as well as a sharp point-wise decay estimate of the solution. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Existence of solutions to a phase transition model with microscopic movements MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2009Eduard FeireislAbstract We prove the existence of weak solutions for a 3D phase change model introduced by Michel Frémond in (Non-smooth Thermomechanics. Springer: Berlin, 2002) showing, via a priori estimates, the weak sequential stability property in the sense already used by the first author in (Comput. Math. Appl. 2007; 53:461,490). The result follows by passing to the limit in an approximate problem obtained adding a superlinear part (in terms of the gradient of the temperature) in the heat flux law. We first prove well posedness for this last problem and then,using proper a priori estimates,we pass to the limit showing that the total energy is conserved during the evolution process and proving the non-negativity of the entropy production rate in a suitable sense. Finally, these weak solutions turn out to be the classical solution to the original Frémond's model provided all quantities in question are smooth enough. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Heat transfer in composite materials with Stefan,Boltzmann interface conditions MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2008Yang GufanAbstract In this paper, we discuss nonstationary heat transfer problems in composite materials. This problem can be formulated as the parabolic equation with Stefan,Boltzmann interface conditions. It is proved that there exists a unique global classical solution to one-dimensional problems. Moreover, we propose a numerical algorithm by the finite difference method for this nonlinear transmission problem. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Boundary integral method for Stokes flow past a porous body MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2008Mirela KohrAbstract In this paper we obtain an indirect boundary integral method in order to prove existence and uniqueness of the classical solution to a boundary value problem for the Stokes,Brinkman-coupled system, which describes an unbounded Stokes flow past a porous body in terms of Brinkman's model. Therefore, one assumes that the flow inside the body is governed by the continuity and Brinkman equations. Some asymptotic results in both cases of large and, respectively, of low permeability are also obtained. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## A direct method for solving an anisotropic mean curvature flow of plane curves with an external force MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2004Karol MikulaAbstract A new method for solution of the evolution of plane curves satisfying the geometric equation v=,(x,k,,), where v is the normal velocity, k and , are the curvature and tangential angle of a plane curve , , ,2 at the point x,,, is proposed. We derive a governing system of partial differential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves and prove local in time existence of a classical solution. These equations include a non-trivial tangential velocity functional governing a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system of equations in order to find a numerical solution for 2D anisotropic interface motions and image segmentation problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Initial boundary value problem for a class of non-linear strongly damped wave equations MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2003Yang ZhijianThe paper studies the existence, asymptotic behaviour and stability of global solutions to the initial boundary value problem for a class of strongly damped non-linear wave equations. By a H00.5ptk-Galerkin approximation scheme, it proves that the above-mentioned problem admits a unique classical solution depending continuously on initial data and decaying to zero as t,+,as long as the non-linear terms are sufficiently smooth; they, as well as their derivatives or partial derivatives, are of polynomial growth order and the initial energy is properly small. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Some estimates for the torsional rigidity of composite rods MATHEMATISCHE NACHRICHTEN, Issue 3 2007Graziano CrastaAbstract A well-known problem in elasticity consists in placing two linearly elastic materials (of different shear moduli) in a given plane domain ,, so as to maximize the torsional rigidity of the resulting rod; moreover, the proportion of these materials is prescribed. Such a problem may not have a classical solution as the optimal design may contain homogenization regions, where the two materials are mixed in a microscopic scale. Then, the optimal torsional rigidity becomes difficult to compute. In this paper we give some different theoretical upper and lower bounds for the optimal torsional rigidity, and we compare them on some significant domains. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Dual- and triple-mode matrix approximation and regression modelling APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 4 2003Stan LipovetskyAbstract We propose a dual- and triple-mode least squares for matrix approximation. This technique applied to the singular value decomposition produces the classical solution with a new interpretation. Applied to regression modelling, this approach corresponds to a regularized objective and yields a new solution with properties of a ridge regression. The results for regression are robust and suggest a convenient tool for the analysis and interpretation of the model coefficients. Numerical results are given for a marketing research data set. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Power concavity on nonlinear parabolic flows COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2005Ki-Ahm LeeOur object in this paper is to show that the concavity of the power of a solution is preserved in the parabolic p -Laplace equation, called power concavity, and that the power is determined by the homogeneity of the parabolic operator. In the parabolic p -Laplace equation for the density u, the concavity of u(p,2)/p is considered, which indicates why the log-concavity has been considered in heat flow, p = 2. In addition, the long time existence of the classical solution of the parabolic p -Laplacian equation can be obtained if the initial smooth data has -concavity and a nondegenerate gradient along the initial boundary. © 2004 Wiley Periodicals, Inc. [source] ## Call admission control in cellular networks: A reinforcement learning solution INTERNATIONAL JOURNAL OF NETWORK MANAGEMENT, Issue 2 2004Sidi-Mohammed SenouciIn this paper, we address the call admission control (CAC) problem in a cellular network that handles several classes of traffic with different resource requirements. The problem is formulated as a semi-Markov decision process (SMDP) problem. We use a real-time reinforcement learning (RL) [neuro-dynamic programming (NDP)] algorithm to construct a dynamic call admission control policy. We show that the policies obtained using our TQ-CAC and NQ-CAC algorithms, which are two different implementations of the RL algorithm, provide a good solution and are able to earn significantly higher revenues than classical solutions such as guard channel. A large number of experiments illustrates the robustness of our policies and shows how they improve quality of service (QoS) and reduce call-blocking probabilities of handoff calls even with variable traffic conditions.,Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Point-wise decay estimate for the global classical solutions to quasilinear hyperbolic systems MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2009Yi ZhouAbstract In this paper, we first consider the Cauchy problem for quasilinear strictly hyperbolic systems with weak linear degeneracy. The existence of global classical solutions for small and decay initial data was established in (Commun. Partial Differential Equations 1994; 19:1263,1317; Nonlinear Anal. 1997; 28:1299,1322; Chin. Ann. Math. 2004; 25B:37,56). We give a new, very simple proof of this result and also give a sharp point-wise decay estimate of the solution. Then, we consider the mixed initial-boundary-value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in the first quadrant. Under the assumption that the positive eigenvalues are weakly linearly degenerate, the global existence of classical solution with small and decay initial and boundary data was established in (Discrete Continuous Dynamical Systems 2005; 12(1):59,78; Zhou and Yang, in press). We also give a simple proof of this result as well as a sharp point-wise decay estimate of the solution. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## A fourth-order parabolic equation in two space dimensions MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2007Changchun LiuAbstract In this paper, we consider an initial-boundary problem for a fourth-order nonlinear parabolic equations. The problem as a model arises in epitaxial growth of nanoscale thin films. Based on the Lp type estimates and Schauder type estimates, we prove the global existence of classical solutions for the problem in two space dimensions. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Polynomial stability of operator semigroups MATHEMATISCHE NACHRICHTEN, Issue 13-14 2006András BátkaiAbstract We investigate polynomial decay of classical solutions of linear evolution equations. For bounded strongly continuous semigroups on a Banach space this property is closely related to polynomial growth estimates of the resolvent of the generator. For systems of commuting normal operators polynomial decay is characterized in terms of the location of the generator spectrum. The results are applied to systems of coupled wave-type equations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Equivalence of weak Dirichlet's principle, the method of weak solutions and Perron's method towards classical solutions of Dirichlet's problem for harmonic functions MATHEMATISCHE NACHRICHTEN, Issue 4 2006Christian G. SimaderAbstract For boundary data , , W1,2(G ) (where G , ,N is a bounded domain) it is an easy exercise to prove the existence of weak L2 -solutions to the Dirichlet problem ",u = 0 in G, u |,G = , |,G". By means of Weyl's Lemma it is readily seen that there is , , C,(G ), ,, = 0 and , = u a.e. in G . On the contrary it seems to be a complicated task even for this simple equation to prove continuity of , up to the boundary in a suitable domain if , , W1,2(G ) , C0(). The purpose of this paper is to present an elementary proof of that fact in (classical) Dirichlet domains. Here the method of weak solutions (resp. Dirichlet's principle) is equivalent to the classical approaches (Poincaré's "sweeping-out method", Perron's method). (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] |