Beyond quenching for singular reaction-diffusion problems
In: Mathematical Methods in the Applied Sciences, Jg. 17 (1994), S. 1-9
Online
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Zugriff:
Let f(u) be twice continuously differentiable on [0, c]) for some constant c such that f(0) > 0,f′ ⩾ 0,f″ ⩾ 0, and limu→cf(u) = ∞. Also, let χ(S) be the characteristic function of the set S. This article studies all solutions u with non-negative ut, in the region where u < c and with continuous ux for the problem: uxx – ut = − f(u)χ({u < c}), 0 < x < a, 0 < t < ∞, subject to zero initial and first boundary conditions. For any length a larger than the critical length, it is shown that if ∫f(u) du < ∞, then as t tends to infinity, all solutions tend to the unique steady-state profile U(x), which can be computed by a derived formula; furthermore, increasing the length a increases the interval where U(x) c by the same amount. For illustration, examples are given.
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Beyond quenching for singular reaction-diffusion problems
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Autor/in / Beteiligte Person: | Chan, C. Y. ; Ke, Lan |
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Zeitschrift: | Mathematical Methods in the Applied Sciences, Jg. 17 (1994), S. 1-9 |
Veröffentlichung: | Wiley, 1994 |
Medientyp: | unknown |
ISSN: | 1099-1476 (print) ; 0170-4214 (print) |
DOI: | 10.1002/mma.1670170102 |
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