TY - JOUR

T1 - Delayed diffusion due to flux limitation

AU - Rosenau, P.

AU - Hagan, P. S.

AU - Northcutt, R. L.

AU - Cohen, D. S.

N1 - Funding Information:
* Research supported by the U.S. D.O.E. under the Applied Mathematical Sciences Research Program KC-07-01-01-0 and under thegrantW-7405-ENG-36,by theU.S. ArmyResearch Office (Durham) undercontract DAALO3-89-K-00 14, by the National Science Foundation under grant DMS-8706642, and by the Air Force Office of Scientific Research under contracts AFSOR-88-0269 and AFSOR-86-0352.

PY - 1989/11/27

Y1 - 1989/11/27

N2 - Consider a flux-limited diffusion process, where ut=[G(ux)]x with G(∞)<∞ and G′(s)≥0. We show that if the pr ofile u(0, x initially has a sharp front, then the sharp front may not be resolved immediately. Instead, the front may remain perfectly sharp for a finite time, during which the height of the jump decays to zero. In this case the profile near the sharp front takes a self-similar form u= tf(x/ t), with the front remaining sharp for a time [h/2f(0)]2, where h is the height of the initial discontinuity . We also determine when an initially sharp jump will remain sharp for a finite time, and when it will be resolved immediately.

AB - Consider a flux-limited diffusion process, where ut=[G(ux)]x with G(∞)<∞ and G′(s)≥0. We show that if the pr ofile u(0, x initially has a sharp front, then the sharp front may not be resolved immediately. Instead, the front may remain perfectly sharp for a finite time, during which the height of the jump decays to zero. In this case the profile near the sharp front takes a self-similar form u= tf(x/ t), with the front remaining sharp for a time [h/2f(0)]2, where h is the height of the initial discontinuity . We also determine when an initially sharp jump will remain sharp for a finite time, and when it will be resolved immediately.

UR - http://www.scopus.com/inward/record.url?scp=38249005870&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(89)90707-X

DO - 10.1016/0375-9601(89)90707-X

M3 - מאמר

AN - SCOPUS:38249005870

VL - 142

SP - 26

EP - 30

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 1

ER -