Critical exponent in a Stefan problem with kinetic condition
In: European Journal of Applied Mathematics, Jg. 8 (1997-10-01), S. 525-532
Online
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Zugriff:
In this paper we deal with the one-dimensional Stefan problemut−uxx =s˙(t)δ(x−s(t)) in ℝ ;× ℝ+, u(x, 0) =u0(x)with kinetic condition s˙(t)=f(u) on the free boundary F={(x, t), x=s(t)}, where δ(x) is the Dirac function. We proved in [1] that if [mid ]f(u)[mid ][les ]Meγ[mid ]u[mid ] for some M>0 and γ∈(0, 1/4), then there exists a global solution to the above problem; and the solution may blow up in finite time if f(u)[ges ] Ceγ1[mid ]u[mid ] for some γ1 large. In this paper we obtain the optimal exponent, which turns out to be √2πe. That is, the above problem has a global solution if [mid ]f(u)[mid ][les ]Meγ[mid ]u[mid ] for some γ∈(0, √2πe), and the solution may blow up in finite time if f(u)[ges ] Ce√2πe[mid ]u[mid ].
Titel: |
Critical exponent in a Stefan problem with kinetic condition
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Autor/in / Beteiligte Person: | Guan, Zhicheng ; Wang, Xu-Jia |
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Zeitschrift: | European Journal of Applied Mathematics, Jg. 8 (1997-10-01), S. 525-532 |
Veröffentlichung: | Cambridge University Press (CUP), 1997 |
Medientyp: | unknown |
ISSN: | 1469-4425 (print) ; 0956-7925 (print) |
DOI: | 10.1017/s0956792597003215 |
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