Results 231 to 240 of about 13,806 (267)
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Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems*
Chinese Annals of Mathematics, Series B, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Decay rate of solutions to hyperbolic system of first order
Acta Mathematica Sinica, 1999Summary: In this paper we generalize global Sobolev inequality introduced by Klainerman in studying wave equation to the hyperbolic system case. We obtain several decay estimate of solutions to hyperbolic system of first order by different norms of initial data. Particularly, the result mentioned in Theorem 1.5 offers an optimal decay rate of solutions,
Chen, Shuxing, Zhou, Yi
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Singularities of solutions for first order quasilinear hyperbolic systems
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1983SynopsisIn this paper, the existence of global smooth solutions and the formation of singularities of solutions for strictly hyperbolic systems with general eigenvalues are discussed for the Cauchy problem with essentially periodic small initial data or nonperiodic initial data. A result of Klainerman and Majda is thus extended to the general case.
Lee, Da-tsin, Shi, Jia-hong
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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 ...
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Necessary Conditions for Hyperbolicity of First Order Systems
2003In this note some necessary conditions for the well posedness of the Cauchy problem for hyperbolic systems of arbitrary order will be studied. In the scalar case Ivrii and Petkov [7] has shown that the well posedness of the Cauchy problem implies that, near a multiple characteristic point, a set of vanishing conditions on the homogeneous parts of the ...
Antonio Bove, Tatsuo Nishitani
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Inverse coefficient problems for a first order hyperbolic system
Applied Numerical Mathematics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ismailov, Mansur I., Tekin, Ibrahim
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Exponential Dichotomy and Time-Bounded Solutions for First-Order Hyperbolic Systems
Journal of Dynamics and Differential Equations, 2002This paper concerns the Cauchy problem \[ D_tu-P_\varepsilon (t,x, D_x)u=f(t,x), \tag{1} \] \[ u(0,x)=u_0(x). \tag{2} \] Here \(\varepsilon \in[-1,1]\) is a parameter, \(x\in\mathbb{R}^n\), \(t\in\mathbb{R}\), and \(P_\varepsilon\) is a strongly hyperbolic first-order differential operator whose coefficients are close to being constant.
Shirikyan, Armen, Volevich, Leonid
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Necessary conditions for strong hyperbolicity of first order systems
Journal d'Analyse Mathématique, 1993The author considers a first order differential operator \(L\) acting on \(C^ \infty(\Omega, \mathbb{C}^ m)\) with Cauchy data on a non- characteristic surface (where \(\Omega\) is a nonempty and open subset in \(\mathbb{R}^{n+1}\)) and gives some necessary conditions in order that \(L+B\) is correctly posed for each \(B\in C^ \infty (\Omega, M_ m ...
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