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Global solution of the pressureless gas equation with viscosity
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-6608-0715
2002 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, Vol. 163, no 3-4, 184-190 p.Article in journal (Refereed) Published
Abstract [en]

We construct a global weak solution to a d-dimensional system of zero-pressure gas dynamics modified by introducing a finite artificial viscosity. We use discrete approximations to the continuous gas and make particles move along trajectories of the normalized simple symmetric random walk with deterministic drift. The interaction of these particles is given by a sticky particle dynamics. We show that a subsequence of these approximations converges to a weak solution of the system of zero-pressure gas dynamics in the sense of distributions. This weak solution is interpreted in terms of a random process solution of a nonlinear stochastic differential equation. We get a weak solution of the inviscid system by tending the viscosity to zero.

Place, publisher, year, edition, pages
2002. Vol. 163, no 3-4, 184-190 p.
Keyword [en]
pressureless gas equations with viscosity, nonlinear diffusion process, weak convergence, sticky
URN: urn:nbn:se:kth:diva-21398ISI: 000174533100004OAI: diva2:340096
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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Djehiche, Boualem
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