Results 241 to 250 of about 224,593 (278)
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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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2003
We study the Cauchy problem for (mainly) first order systems. Our main concern is to investigate for which systems the Cauchy problem is C ∞ well posed for any lower order terms (strong hyperbolicity), or for which systems the Cauchy problem is C ∞ well posed (hyperbolicity).
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We study the Cauchy problem for (mainly) first order systems. Our main concern is to investigate for which systems the Cauchy problem is C ∞ well posed for any lower order terms (strong hyperbolicity), or for which systems the Cauchy problem is C ∞ well posed (hyperbolicity).
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1990
In this chapter we begin the study of systems of conservation laws by reviewing the theory of a constant coefficient linear hyperbolic system. Here we can solve the equations explicitly by transforming to characteristic variables. We will also obtain explicit solutions of the Riemann problem and introduce a “phase space” interpretation that will be ...
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In this chapter we begin the study of systems of conservation laws by reviewing the theory of a constant coefficient linear hyperbolic system. Here we can solve the equations explicitly by transforming to characteristic variables. We will also obtain explicit solutions of the Riemann problem and introduce a “phase space” interpretation that will be ...
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Convergence of first-order quasilinear hyperbolic systems to hyperbolic-parabolic systems
Nonlinear AnalysiszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yue-Jun Peng, Shuimiao Du
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1991
In this chapter we treat various types of hyperbolic equations, beginning in §5.1 with first order symmetric hyperbolic systems. In this case, little direct use of pseudodifferential operator techniques is made, mainly an appeal to the Kato-Ponce estimates.
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In this chapter we treat various types of hyperbolic equations, beginning in §5.1 with first order symmetric hyperbolic systems. In this case, little direct use of pseudodifferential operator techniques is made, mainly an appeal to the Kato-Ponce estimates.
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Hyperbolic Monge-Ampère systems
Sbornik: Mathematics, 2006The subject of the paper is the solubility of the Cauchy problem for strictly hyperbolic systems of Monge-Ampere equations and, in particu- lar, for quasilinear systems of equations with two independent variables. It is proved that this problem has a unique maximal solution in the class of immersed many-valued solutions.
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2015
Wave propagation phenomena give us an important mean to check the validation of the nonequilibrium thermodynamics theory. In this chapter, we present a short review on the modern theory of wave propagation for hyperbolic systems. Firstly, we present the theory of linear waves emphasizing the role of the dispersion relation.
Tommaso Ruggeri, Masaru Sugiyama
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Wave propagation phenomena give us an important mean to check the validation of the nonequilibrium thermodynamics theory. In this chapter, we present a short review on the modern theory of wave propagation for hyperbolic systems. Firstly, we present the theory of linear waves emphasizing the role of the dispersion relation.
Tommaso Ruggeri, Masaru Sugiyama
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Hyperbolic metamaterials: fusing artificial structures to natural 2D materials
ELight, 2022Dasol Lee, Sunae So, Guangwei Hu
exaly
Linear symmetric hyperbolic systems
1992Let \(u=u(t,x)=(u_1,\ldots,u_{N})(t,x), t\geq 0,x \in \mathrm{I}\!\mathrm{R}^{n}, N \in \mathrm{I}\!\mathrm{N}\), and let the formal linear differential operator L be defined by $$Lu := A^{0}(t,x)\partial_{t}u + \sum\limits^{n}_{j=1}A^{j}(t,x)\partial_{j}u + B(t,x)u$$ .
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