Results 181 to 190 of about 22,806,811 (229)
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AN INHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEM
Acta Mathematica Scientia, 1981Abstract : We consider quasilinear hyperbolic partial differential equations modeling ideal gas flow under various physical effects. When these effects are represented as Lipschitz continuous functions of the states, solutions to the initial value problem are shown to exist globally in time.
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Quasilinear hyperbolic systems with involutions
Archive for Rational Mechanics and Analysis, 1986The author considers quasilinear hyperbolic systems \[ (1)\quad \partial_ tU+\sum^{m}_{\alpha =1}\partial_{\alpha}G_{\alpha}(U)=0 \] where \(x\in {\mathbb{R}}^ m\), the vector U(x,t) takes values in an open subset \({\mathcal O}\subset {\mathbb{R}}^ n\) and \(G_{\alpha}: {\mathcal O}\to {\mathbb{R}}^ n\) are given smooth functions. A classical solution
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Stability Criteria for Quasilinear Impulsive Systems
International Applied Mechanics, 2004The authors establish stability conditions for quasilinear large-scale systems with impulsive effect in the cases when the known approaches to stability investigation of such systems can not be applied. An efficient technique of analysis of uncertain impulsive systems is proposed which admits an extension to some classes of interval systems.
Dvirny, A. I., Slyn'ko, V. I.
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First-order quasilinear systems
2003Abstract When we use vector systems of partial differential equations, we can model many more physical situations than when we are restricted to the scalar case. For example, as well as looking at the simple kinematic wave models of Chapter 1, we can study situations which allow simultaneous wave propagation both backwards and forwards ...
John Ockendon +3 more
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On optimal control over quasilinear systems
Ukrainian Mathematical Journal, 1995Author studies the approximation method for the optimal stabilization control of the quasilinear system \(\dot x=Ax+Du+\mu \varphi (x)\), where \(\mu\) is a small parameter, \(A\) and \(D\) are matrices, the function \(\varphi (x)\) is analytic in some bounded domain, components of the vector-valued function \(x(t,\mu)\) are absolutely continuous ...
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State observation for heterogeneous quasilinear traffic flow system with disturbances
MCSS. Mathematics of Control, Signals and Systems, 2023Lina Guan +3 more
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A Parabolic-Hyperbolic Quasilinear System
Communications in Partial Differential Equations, 2008We prove the existence and uniqueness of solutions of the parabolic–hyperbolic system for unknown (u,φ) = (u(x,t),φ(x,t)), where Ω is a bounded domain in ℝ n with smooth boundary. The system is solved subject to no-flux boundary condition for φ and given initial conditions for u and φ. Structural conditions on F and G are assumed to ensure L ∞ a priori
Xinfu Chen, Avner Friedman, Bei Hu
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Quasilinearization, system identification and prediction
International Journal of Engineering Science, 1965Abstract This paper is devoted to a mathematical formulation and computational solution of the problems of system identification and the determination of unmeasurable state variables on the basis of observations of a process, two topics of central importance in the design of adaptive controllers.
Bellman, R., Kagiwada, H., Kalaba, R.
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Decay rate and blow up solutions for coupled quasilinear system
Boletín de la Sociedad Matematica Mexicana, 2020N. Mezouar, E. Pişkin
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Semilinear and quasilinear systems
2000Abstract A quasilinear system of n equations in one space variable takes the form By a classical solution of (3.1) we mean a continuously differentiable function u = uft, x) which satisfies (3.1) at every point of its domain. In later sections, we shall also consider broad solutions, corresponding to fixed points of a suitable integral ...
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