Instantaneous Filling of the Vacuum for the Full Boltzmann Equation in Convex Domains
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| 008 | 210128e20151101xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0874-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0874-x | ||
| 100 | 1 | |a Briant |D M. |u Centre for Mathematical Sciences, University of Cambridge DPMMS, Wilberforce Road, CB3 0WA, Cambridge, UK |4 aut | |
| 245 | 1 | 0 | |a Instantaneous Filling of the Vacuum for the Full Boltzmann Equation in Convex Domains |h [Elektronische Daten] |c [M. Briant] |
| 520 | 3 | |a We prove the immediate appearance of a lower bound for mild solutions to the full Boltzmann equation in the torus or a C 2 convex domain with specular boundary conditions, under the sole assumption of continuity away from the grazing set of the solution. These results are entirely constructive if the domain is C 3 and strictly convex. We investigate a wide range of collision kernels, some satisfying Grad's cutoff assumption and others not. We show that this lower bound is exponential, independent of time and space with explicit constants depending only on the a priori bounds on the solution. In particular, this lower bound is Maxwellian in the case of cutoff collision kernels. A thorough study of characteristic trajectories, as well as a geometric approach of grazing collisions against the boundary are derived. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 985-1041 |x 0003-9527 |q 218:2<985 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0874-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0874-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Briant |D M. |u Centre for Mathematical Sciences, University of Cambridge DPMMS, Wilberforce Road, CB3 0WA, Cambridge, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 985-1041 |x 0003-9527 |q 218:2<985 |1 2015 |2 218 |o 205 | ||