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1.
We study the focusing problem for the eikonal equation¶¶ ?tu=| ?u| 2, \partial _{t}u=\left| \nabla u\right| ^{2}, ¶¶i.e., the initial value problem in which the support of the initial datum is outside some compact set in Rd \mathbf{R}^{d} . The hole in the support will be filled in finite time and we are interested in the asymptotics of the hole as it closes. We show that in the radially symmetric case there are self-similar asymptotics, while in the absence of radial symmetry essentially any convex final shape is possible. However in R2 \mathbf{R}^2 , for generic initial data the asymptotic shape will be either a vanishing triangle or the region between two parabolas moving in opposite directions (a closing eye). We compare these results with the known results for the porous medium pressure equation which approaches the eikonal equation in the limit as m? 1 m\rightarrow 1 . 相似文献
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Abe K Ahrens LA Amako K Aronson SH Beier EW Callas JL Cutts D Diwan M Durkin LS Gibbard BG Heagy SM Hedin D Hoftun JS Hurley M Kabe S Kurihara Y Lanou RE Mann AK Marx MD Murtagh MJ Nagashima Y Newcomer FM Shinkawa T Stern E Suzuki Y Terada S White DH Williams HH Yamaguchi Y 《Physical review letters》1987,58(7):636-639
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Abachi S Abbott B Abolins M Acharya BS Adam I Adams DL Adams M Ahn S Aihara H Alitti J Álvarez G Alves GA Amidi E Amos N Anderson EW Aronson SH Astur R Avery RE Baarmand MM Baden A Balamurali V Balderston J Baldin B Banerjee S Bantly J Bartlett JF Bazizi K Bendich J Beri SB Bertram I Bezzubov VA Bhat PC Bhatnagar V Bhattacharjee M Bischoff A Biswas N Blazey G Blessing S Bloom P Boehnlein A Bojko NI Borcherding F Borders J Boswell C Brandt A Brock R Bross A Buchholz D Burtovoi VS Butler JM 《Physical review letters》1996,77(4):595-600
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Abachi S Abbott B Abolins M Acharya BS Adam I Adams DL Adams M Ahn S Aihara H Alitti J Álvarez G Alves GA Amidi E Amos N Anderson EW Aronson SH Astur R Avery RE Baarmand MM Baden A Balamurali V Balderston J Baldin B Banerjee S Bantly J Bartlett JF Bazizi K Bendich J Beri SB Bertram I Bezzubov VA Bhat PC Bhatnagar V Bhattacharjee M Bischoff A Biswas N Blazey G Blessing S Bloom P Boehnlein A Bojko NI Borcherding F Borders J Boswell C Brandt A Brock R Bross A Buchholz D Burtovoi VS Butler JM 《Physical review letters》1996,77(25):5011-5015
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Abachi S Abbott B Abolins M Acharya BS Adam I Adams DL Adams M Ahn S Aihara H Alitti J Álvarez G Alves GA Amidi E Amos N Anderson EW Aronson SH Astur R Avery RE Baden A Balamurali V Balderston J Baldin B Bantly J Bartlett JF Bazizi K Bendich J Beri SB Bertram I Bezzubov VA Bhat PC Bhatnagar V Bhattacharjee M Bischoff A Biswas N Blazey G Blessing S Bloom P Boehnlein A Bojko NI Borcherding F Borders J Boswell C Brandt A Brock R Bross A Buchholz D Burtovoi VS Butler JM Carvalho W Casey D 《Physical review letters》1996,76(18):3271-3276
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Adler SS Afanasiev S Aidala C Ajitanand NN Akiba Y Alexander J Amirikas R Aphecetche L Aronson SH Averbeck R Awes TC Azmoun R Babintsev V Baldisseri A Barish KN Barnes PD Bassalleck B Bathe S Batsouli S Baublis V Bazilevsky A Belikov S Berdnikov Y Bhagavatula S Boissevain JG Borel H Borenstein S Brooks ML Brown DS Bruner N Bucher D Buesching H Bumazhnov V Bunce G Burward-Hoy JM Butsyk S Camard X Chai JS Chand P Chang WC Chernichenko S Chi CY Chiba J Chiu M Choi IJ Choi J Choudhury RK Chujo T 《Physical review letters》2004,93(9):092301
Event-by-event fluctuations of the average transverse momentum of produced particles near midrapidity have been measured by the PHENIX Collaboration in square root of (sNN)=200 GeV Au+Au, and p+p collisions at the Relativistic Heavy Ion Collider. The fluctuations are observed to be in excess of the expectation for statistically independent particle emission for all centralities. The excess fluctuations exhibit a dependence on both the centrality of the collision and on the pT range over which the average is calculated. Both the centrality and pT dependence can be well reproduced by a simulation of random particle production with the addition of contributions from hard-scattering processes. 相似文献