NUMERICAL BLOW-UP FOR A NONLINEAR PROBLEM WITH A NONLINEAR BOUNDARY CONDITION
2002 ◽
Vol 12
(04)
◽
pp. 461-483
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Keyword(s):
Blow Up
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In this paper we study numerical approximations for positive solutions of a nonlinear heat equation with a nonlinear boundary condition. We describe in terms of the nonlinearities when solutions of a semidiscretization in space exist globally in time and when they blow up in finite time. We also find the blow-up rates and the blow-up sets. In particular we prove that regional blow-up is not reproduced by the numerical scheme. However, in the appropriate variables we can reproduce the correct blow-up set when the mesh parameter goes to zero.
1991 ◽
Vol 92
(2)
◽
pp. 384-401
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Keyword(s):
2009 ◽
Vol 139
(6)
◽
pp. 1289-1296
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2002 ◽
Vol 48
(7)
◽
pp. 995-1002
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Keyword(s):
1999 ◽
Vol 48
(1)
◽
pp. 135-152
Keyword(s):
1989 ◽
Vol 69
(1)
◽
pp. 51-52
◽
Keyword(s):