Search results for "Linear system"
showing 10 items of 1558 documents
Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements
2010
The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences. This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods. That is why we use an alternative approach and solve the time-harmonic problem by controlling the solution of the corresponding time dependent wave equation. In this paper, we use an unsymmetric formulation, where fluid-structure interaction is modeled as a coupling between pressure and displacement. The coupled problem is discretized in space domain with spectral el…
Controllable Solid Rocket Motor Nozzle Operations in Conditions of Limited-Amplitude Fluctuations
2009
A nonlinear multi scale analysis of a controllable solid rocket motor operating in conditions ranging from high-amplitude fluctuations in combustion chamber to conditions lying in limit cycle is presented and the motor behavior subsequent to some relevant nozzle operations is investigated. Effects of acoustic-vorticity-entropy wave coupling, wave steepening, rotational/viscous flow losses, steep-fronted wave losses are taken into account and oscillatory energy losses in pintle-nozzle, unsteady combustion and chamber geometry changes resulting from grain regression are included. The analysis provides evidence that the unsteady energy balance and the motor wave amplitude evolution are influen…
Quantized State-Feedback Stabilization for Delayed Markovian Jump Linear Systems with Generally Incomplete Transition Rates
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/961925 open Access This paper is concerned with the robust quantized state-feedback controller design problem for a class of continuous-time Markovian jump linear uncertain systems with general uncertain transition rates and input quantization. The uncertainties under consideration emerge in both system parameters and mode transition rates. This new uncertain model is more general than the existing ones and can be applicable to more practical situations because each transition rate can be completely unknown or only its estimate value is known. B…
Singular Double Phase Problems with Convection
2020
We consider a nonlinear Dirichlet problem driven by the sum of a $p$ -Laplacian and of a $q$ -Laplacian (double phase equation). In the reaction we have the combined effects of a singular term and of a gradient dependent term (convection) which is locally defined. Using a mixture of variational and topological methods, together with suitable truncation and comparison techniques, we prove the existence of a positive smooth solution.
Positive solutions for nonlinear Robin problems with convection
2019
We consider a nonlinear Robin problem driven by the p-Laplacian and with a convection term f(z,x,y). Without imposing any global growth condition on f(z,·,·) and using topological methods (the Leray-Schauder alternative principle), we show the existence of a positive smooth solution.
Variable exponent p(x)-Kirchhoff type problem with convection
2022
Abstract We study a nonlinear p ( x ) -Kirchhoff type problem with Dirichlet boundary condition, in the case of a reaction term depending also on the gradient (convection). Using a topological approach based on the Galerkin method, we discuss the existence of two notions of solutions: strong generalized solution and weak solution. Strengthening the bound on the Kirchhoff type term (positivity condition), we establish existence of weak solution, this time using the theory of operators of monotone type.
Linearly implicit-explicit schemes for the equilibrium dispersive model of chromatography
2018
Abstract Numerical schemes for the nonlinear equilibrium dispersive (ED) model for chromatographic processes with adsorption isotherms of Langmuir type are proposed. This model consists of a system of nonlinear, convection-dominated partial differential equations. The nonlinear convection gives rise to sharp moving transitions between concentrations of different solute components. This property calls for numerical methods with shock capturing capabilities. Based on results by Donat, Guerrero and Mulet (Appl. Numer. Math. 123 (2018) 22–42), conservative shock capturing numerical schemes can be designed for this chromatography model. Since explicit schemes for diffusion problems can pose seve…
Constrained control of a nonlinear two point boundary value problem, I
1994
In this paper we consider an optimal control problem for a nonlinear second order ordinary differential equation with integral constraints. A necessary optimality condition in form of the Pontryagin minimum principle is derived. The proof is based on McShane-variations of the optimal control, a thorough study of their behaviour in dependence of some denning parameters, a generalized Green formula for second order ordinary differential equations with measurable coefficients and certain tools of convex analysis.
Nonsmooth Mechanics. Convex and Nonconvex Problems
1999
Nonlinear, multivalued and possibly nonmonotone relations arise in several areas of mechanics. A multivalued or complete relation is a relation with complete vertical branches. Boundary laws of this kind connect boundary (or interface) quantities. A contact relation or a locking mechanism between boundary displacements and boundary tractions in elasticity is a representative example. Material constitutive relations with complete branches connect stress and strain tensors, or, in simplified theories, equivalent stress and strain quantities. A locking material or a perfectly plastic one is represented by such a relation. The question of nonmonotonicity is more complicated. One aspect concerns…
Monotonicity and enclosure methods for the p-Laplace equation
2018
We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the $p$-conductivity equation is determined by knowledge of the nonlinear Dirichlet-Neumann operator. We give two independent proofs, one of which is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.