Bifurcation analysis and soliton solutions of the generalized third-order nonlinear Schrödinger equation using two analytical approaches. [PDF]
Parveen S +6 more
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On the boundary controllability of first-order hyperbolic systems
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ANCONA F, COCLITE, Giuseppe Maria
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An explicit mapping from linear first order hyperbolic PDEs to difference systems
Systems and Control Letters, 2019In this paper, we prove that the space generated by the solutions of a general class of first-order hyperbolic PDEs is isomorphic to the space generated by the solutions of a difference equation with distributed delays.
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Tangential Characteristic Symmetries and First Order Hyperbolic Systems
Applicable Algebra in Engineering, Communication and Computing, 2001The systems studied here comprise two equations for two functions of two variables. Such a system is assumed to define a smooth submanifold \({\mathcal R}^6 \subset J^1({\mathbb R}^2,{\mathbb R}^2)\), equipped with a smooth codimension-two distribution \(\Sigma\) to which the 1-graph of any solution is tangent; hyperbolicity gives a canonical splitting
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A first-order hyperbolic reformulation of the Cahn-Hilliard equation
In this paper we present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques proposed earlier by the authors of this paper, with a classical Cattaneo-type
Firas Dhaouadi, M. Dumbser, S. Gavrilyuk
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Convergence of first-order quasilinear hyperbolic systems to hyperbolic-parabolic systems
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yue-Jun Peng, Shuimiao Du
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Singular Perturbations of First-Order Hyperbolic Systems
1993This work develops the singular perturbation theory for initial-value problems of nonlinear first-order hyperbolic systems in several space variables. The results can be applied to many physical problems in the kinetic theory, MHD, gas dynamics with relaxation, inviscid reactive flow, traffic flow, river flow, glacier flow, certain chemical exchange ...
W. Yong
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Least‐squares finite elements for first‐order hyperbolic systems
International Journal for Numerical Methods in Engineering, 1988AbstractA class of least‐squares finite element methods has been developed for first‐order systems and here we study this approach for hyperbolic problems. The formulation of the least‐squares method is developed in detail and compared with the Petrov‐Galerkin and Taylor‐Galerkin procedures.
Carey, Graham F., Jiang, B. N.
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Asymptotic integration of first-order hyperbolic systems
Lithuanian Mathematical Journal, 1984This paper deals with the two dimensional Cauchy problem: \[ \partial u_ j/\partial t+\lambda_ j(\partial u_ j/\partial x)=\epsilon f_ j(u_ 1,...,u_ n) \] \[ u_ j(0,x,\epsilon)=u_{j0}(x)+(\sum^{k}_{i=1}\epsilon^ iu_{ji}(x))+\epsilon^{k+1}u_{jk+1}(x,\epsilon) \] involving a small parameter \(\epsilon >0\) and real numbers \(\lambda_ 1,...,\lambda_ n ...
A. Krylov
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Iterative learning control with high-order internal model for first-order hyperbolic systems.
ISA transactions, 2021This paper studies the iterative learning control (ILC) algorithm for first-order hyperbolic systems. Unlike most of the ILC literature of distributed parameter systems, in the iteration domain, that require identical desired trajectories.
Panpan Gu, Senping Tian
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