Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics
Springer INdAM Series, 2017 The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015.
Lannes, David +3 more
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Evolution of interface singularities in shallow water equations with variable bottom topography [PDF]
, 2022 Wave front propagation with nontrivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of nonsmooth initial data is examined, and, in particular, the splitting of singular points and their short time behavior ...
Ortenzi, Giovanni, Pedroni, Marco
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On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations [PDF]
, 2015 We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components.
Klein, Christian +13 more
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Meromorphy and topology of localized solutions in the Thomas–MHD model [PDF]
, 2001 The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number.
Fournier, J.D. +2 more
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HAMILTONIAN SHOCKS AND OTHER SINGULAR FRONTS IN HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
, 2023 The nature of wave interaction in a continuum dynamical model may undergo a qualitative change in certain asymptotic regimes, most notably when linearity or complete integrability is introduced. This occurs in particular when the mKdV equation is used to
Arnold, Russell
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Shock formation in small-data solutions to 3D quasilinear wave equations
, 2016 In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity.
Speck, Jared, Jared Speck
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A note on critical times of $2\times2$ quasilinear hyperbolic systems
, 1984 summary:In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a $2\times2$ quasilinear hyperbolic system is derived.
Straškraba, Ivan
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Development of singularities in Riemann Invariants
, 1992 Shocks form in finite time in systems of quasilinear hyperbolic equations in one space variable which are genuinely nonlinear. The authors write down a simple geometric construction for systems of two equations, and use it to obtain a priori estimates ...
Keyfitz, B.L.
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REGULARIZATION OF SINGULAR SOURCES FOR PSIC COMPUTATIONS OF PARTICLE-LADEN FLOWS WITH SHOCKS [PDF]
, 2015 Includes bibliographical references (pages 72-76In this dissertation we develop a high-order regularization technique with optimal\ud scaling to approximate singular sources expressed as one single Dirac-delta or\ud weighted summation of Dirac-deltas. We
Suarez Solano, Jean Piero
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Eulerian Droplet Models: Mathematical Analysis, Improvement and Applications
, 2018 The Eulerian description of dispersed two-phase flows results in a system of partial differential equations describing characteristics of the flow, namely volume fraction, density and velocity of the two phases, around any point in space over time ...
Keita, Sana
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