Well Posedness for Pressureless Flow

Huang, Feimin; Wang, Zhen

doi:10.1007/s002200100506

Cited by 195 publications

(176 citation statements)

References 11 publications

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“…This theory was introduced in [9], and later extended in [10] and [20] (see also [16] and [15]). We cite below the main result of [20], where M 1 (R) denotes the space of Radon measures on R and L 2 (ρ) for ρ ≥ 0 in M 1 (R) denotes the space of functions which are square integrable against ρ. …”

Section: Pressureless Eulermentioning

confidence: 99%

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Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

Jabin

Rey

2016

Quart. Appl. Math.

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Abstract. We investigate the behavior of granular gases in the limit of small Knudsen number, that is very frequent collisions. We deal with the strongly inelastic case, in one dimension of space and velocity. We are able to prove the convergence toward the pressureless Euler system. The proof relies on dispersive relations at the kinetic level, which leads to the so-called Oleinik property at the limit.

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Section: Pressureless Eulermentioning

confidence: 99%

“…In that case one knows in addition that the limit is the unique "sticky particles" solution to the pressureless system (1.4) as obtained in [9,20] The basic idea of the proof of Th. 1.3 is to use the kinetic description (1.15) to compare the granular gases dynamics to pressureless gas system.…”

Section: Remarkmentioning

confidence: 99%

Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

Jabin

Rey

2016

Quart. Appl. Math.

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“…Special attentions were also paid in [12,16,17,24,31,33,35,37,38] to the formation of the delta shock waves in the Riemann solutions for some hyperbolic systems of conservation laws. There exist numerous excellent papers for the related equations and results about the measure-valued solutions such as the delta shock wave for hyperbolic systems of conservation laws, see [6,15,18,23,25,26] for instance.…”

Section: Introductionmentioning

confidence: 99%

The Delta Standing Wave Solution for the Linear Scalar Conservation Law With Discontinuous Coefficients Using a Self-Similar Viscous Regularization

Li¹,

Shen²

2015

Bulletin of the Korean Mathematical Society

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Abstract. This paper is mainly concerned with the formation of delta standing wave for the scalar conservation law with a linear flux function involving discontinuous coefficients by using the self-similar viscosity vanishing method. More precisely, we use the self-similar viscosity to smooth out the discontinuous coefficient such that the existence of approximate viscous solutions to the delta standing wave for the Riemann problem is established and then the convergence to the delta standing wave solution is also obtained when the viscosity parameter tends to zero. In addition, the Riemann problem is also solved with the standard method and the instability of Riemann solutions with respect to the specific small perturbation of initial data is pointed out in some particular situations.

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“…the transport equations 6) which are called the one-dimensional system of pressureless Euler equations. The transport equations (1.6) have been analyzed extensively, see [5,8,14,15,[19][20][21]35,41] and so on. Recently, the weak asymptotics method was widely used to study the δ-shock wave type solution by Danilov et al [12,13,29,32,40] in the case of systems which are linear with respect to one of unknown functions.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional nonlinear chromatography system and delta-shock waves

2013

Z. Angew. Math. Phys.

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Abstract. The Riemann problem for the nonlinear chromatography system is considered. Existence and admissibility of δ-shock type solution in both variables are established for this system. By the interactions of δ-shock wave with elementary waves, the generalized Riemann problem for this system is presented, the global solutions are constructed, and the large time-asymptotic behavior of the solutions are analyzed. Moreover, by studying the limits of the solutions as perturbed parameter ε tends to zero, one can observe that the Riemann solutions are stable for such perturbations of the initial data.Mathematics Subject Classification. 35L65 · 35L67 · 35J70.

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Well Posedness for Pressureless Flow

Cited by 195 publications

References 11 publications

Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

Hydrodynamic limit of granular gases to pressureless Euler in dimension 1

The Delta Standing Wave Solution for the Linear Scalar Conservation Law With Discontinuous Coefficients Using a Self-Similar Viscous Regularization

One-dimensional nonlinear chromatography system and delta-shock waves

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