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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High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling [PDF]
, 2014 Copyright @ 2014 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.We revisit a method ...
Mark P Brewin +19 more
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Continuity equations and ODE flows with non-smooth velocity [PDF]
, 2014 In this paper we review many aspects of the well-posedness theory for the Cauchy problem for the continuity and transport equations and for the ordinary differential equation (ODE). In this framework, we deal with velocity fields that are not smooth, but
Crippa, Gianluca, Ambrosio, Luigi
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Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]
, 2009 Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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Efficient explicit time integration for the simulation of acoustic and electromagnetic waves [PDF]
, 2015 The efficient and accurate numerical simulation of time-dependent wave phenomena is of fundamental importance in acoustic, electromagnetic or seismic wave propagation.
Mehlin, Michaela
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Metric Based Upscaling for Partial Differential Equations with a Continuum of Scales [PDF]
, 2007 Numerical upscaling of problems with multiple scale structures have attracted increasing attention in recent years. In particular, problems with non-separable scales pose a great challenge to mathematical analysis and simulation.
Zhang, Lei
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On the well-posedness of weakly hyperbolic equations with time-dependent coefficients [PDF]
, 2012 30.10.12 KB.
Garetto, Claudia +7 more
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Fourth order Schr\"odinger equation with mixed dispersion on certain Cartan-Hadamard manifolds
, 2022 We study the fourth order Schr\"odinger equation with mixed dispersion on an $N$-dimensional Cartan-Hadamard manifold. At first, we focus on the case of the hyperbolic space.
Casteras, Jean-Baptiste +1 more
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Flows of singular vector fields and applications to fluid and kinetic equations [PDF]
, 2015 Several physical phenomena arising in fluid dynamics and kinetic equations can be modeled by nonlinear transport PDE. Such quantities are the vorticity of a fluid, or the density of a collection of particles advected by a velocity field which is highly ...
Bohun, Anna
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Continuity of solutions of a quasilinear hyperbolic equation with hysteresis [PDF]
, 2012 summary:This paper is devoted to the investigation of quasilinear hyperbolic equations of first order with convex and nonconvex hysteresis operator. It is shown that in the nonconvex case the equation, whose nonlinearity is caused by the hysteresis term,
Kordulová, Petra
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