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On the strongly hyperbolic systems : a reduction of hyperbolic matrices
, 1988 openaire +1 more source
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On the Darboux Problem for Hyperbolic Systems
Differential Equations, 2023For a hyperbolic system with simple characteristics in the-dimensional space of independent variables, the existence and uniqueness of a solution of the Darboux problem is proved. The Riemann–Hadamard matrix is determined, and the solution of the Darboux problem is constructed in terms of this matrix.
Mironov, A. N., Mironova, L. B.
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PARTIALLY HYPERBOLIC DYNAMICAL SYSTEMS
Mathematics of the USSR-Izvestiya, 1974Smooth dynamical systems having contracting and expanding invariant foliations (of not necessarily complementary dimensions) are investigated. Ergodicity and the K-property are established for such dynamical systems under additional assumptions.
Brin, M. I., Pesin, Ya. B.
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1994
Abstract Extended summary of the contribution given at the SERC Numerical Analysis Summer School, Lancaster University, July 1992.) A large variety of physical phenomena is described by hyperbolic systems. Fluid dynamics is probably the field of major relevance: compressible flows (unsteady and steady supersonic), shallow waters ...
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Abstract Extended summary of the contribution given at the SERC Numerical Analysis Summer School, Lancaster University, July 1992.) A large variety of physical phenomena is described by hyperbolic systems. Fluid dynamics is probably the field of major relevance: compressible flows (unsteady and steady supersonic), shallow waters ...
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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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On pseudosymmetric hyperbolic systems
1997The authors investigate first-order weakly hyperbolic systems of PDEs with coefficients depending only on \(t\). The system is supposed to be pseudosymmetric according to a given definition (e.g., in two space dimensions, the system with the matrix \(A=(a_{ij})\) is pseudosymmetric iff \(a_{ii}\) are real and \(a_{12} \cdot a_{21} >0)\).
D'ANCONA, Piero Antonio, S. SPAGNOLO
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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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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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Central Schemes for Nonconservative Hyperbolic Systems
SIAM Journal on Scientific Computing, 2012Summary: We present a new approach to the construction of high order finite volume central schemes on staggered grids for general hyperbolic systems, including those not admitting a conservation form. The method is based on finite volume space discretization on staggered cells, central Runge-Kutta time discretization, and integration over a family of ...
Manuel J. Castro +3 more
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