Internal layers, small eigenvalues, and the sensitivity of metastable motion

Journal Article · Sat Apr 01 04:00:00 EST 1995 · SIAM Journal of Applied Mathematics

DOI:https://doi.org/10.1137/S0036139993269254· OSTI ID:46112

Ward, M J ^[1]; Reyna, L G ^[2]

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1. Univ. of British Columbia, Vancouver (Canada). Dept. of Mathematics
2. I.B.M. Thomas J. Watson Research Center, Yorktown Heights, NY (United States). Mathematical Sciences

On a semi-infinite domain, an analytical characterization of exponentially slow internal layer motion for the Allen Cahn equation and for a singularly perturbed viscous shock problem is given. The results extend some previous results that were restricted to a finite geometry. For these slow motion problems, the authors show that the slow dynamics associated with the semi-infinite domain are not preserved, even qualitatively, by imposing a commonly used form of artificial boundary condition to truncate the semi-infinite domain to a finite domain. This extreme sensitivity to boundary conditions and domain truncation is a direct result of the exponential ill-conditioning of the underlying linearized problem. For Burgers equation, many of the analytical results are verified by calculating certain explicit solutions. Some related ill-conditioned internal layer problems are examined.

• Sponsoring Organization: USDOE
• DOE Contract Number: FG02-88ER25053
• OSTI ID: 46112
• Journal Information: SIAM Journal of Applied Mathematics, Journal Name: SIAM Journal of Applied Mathematics Journal Issue: 2 Vol. 55; ISSN SMJMAP; ISSN 0036-1399
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ANALYTICAL SOLUTION
BOUNDARY-VALUE PROBLEMS
NONLINEAR PROBLEMS
SHOCK WAVES
USES
VERIFICATION