×

Nonlinear stability of the initial-boundary value problem for the Broadwell model around a Maxwellian. (English) Zbl 1227.82062

Author’s abstract: We study the nonlinear stability of the equilibrium state associated with the initial boundary value problem for the Broadwell model with transonic boundary. Based on the Green’s function of this linearized initial boundary value problem and on the understanding of its action on microscopic data, we establish the pointwise convergence of the solution toward the equilibrium state under small perturbation, via a solution representation and Picard-like iterations.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1002/cpa.3160330506 · Zbl 0424.76060 · doi:10.1002/cpa.3160330506
[2] DOI: 10.1002/cpa.3160320502 · Zbl 0438.76059 · doi:10.1002/cpa.3160320502
[3] DOI: 10.3934/nhm.2007.2.383 · Zbl 1140.82028 · doi:10.3934/nhm.2007.2.383
[4] DOI: 10.1016/j.na.2007.10.020 · Zbl 1159.82013 · doi:10.1016/j.na.2007.10.020
[5] DOI: 10.1007/s002200050730 · Zbl 0983.82015 · doi:10.1007/s002200050730
[6] DOI: 10.1007/s002200050808 · Zbl 0981.76079 · doi:10.1007/s002200050808
[7] DOI: 10.3934/nhm.2006.1.167 · Zbl 1111.82047 · doi:10.3934/nhm.2006.1.167
[8] DOI: 10.1142/S0219891608001489 · Zbl 1152.35016 · doi:10.1142/S0219891608001489
[9] DOI: 10.1002/cpa.20011 · Zbl 1111.76047 · doi:10.1002/cpa.20011
[10] DOI: 10.1002/(SICI)1097-0312(199711)50:11<1113::AID-CPA3>3.0.CO;2-D · Zbl 0902.35069 · doi:10.1002/(SICI)1097-0312(199711)50:11<1113::AID-CPA3>3.0.CO;2-D
[11] Liu T.-P., Bull. Inst. Math. Acad. Sin. (N.S.) 1 pp 1–
[12] DOI: 10.1002/cpa.20172 · Zbl 1154.35015 · doi:10.1002/cpa.20172
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.