Blow up of solutions of semilinear heat equations in general domains
2015 ◽
Vol 17
(02)
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pp. 1350042
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Keyword(s):
Blow Up
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Consider the nonlinear heat equation vt - Δv = |v|p-1v in a bounded smooth domain Ω ⊂ ℝn with n > 2 and Dirichlet boundary condition. Given up a sign-changing stationary classical solution fulfilling suitable assumptions, we prove that the solution with initial value ϑup blows up in finite time if |ϑ - 1| > 0 is sufficiently small and if p is sufficiently close to the critical exponent [Formula: see text]. Since for ϑ = 1 the solution is global, this shows that, in general, the set of the initial data for which the solution is global is not star-shaped with respect to the origin. This phenomenon had been previously observed in the case when the domain is a ball and the stationary solution is radially symmetric.
2002 ◽
Vol 04
(03)
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pp. 409-434
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2015 ◽
Vol 08
(01)
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pp. 1550004
2021 ◽
Keyword(s):
1996 ◽
Vol 39
(1)
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pp. 81-96
2018 ◽
Vol 29
(02)
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pp. 1850008
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2002 ◽
Vol 04
(03)
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pp. 547-558
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2002 ◽
Vol 12
(04)
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pp. 461-483
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2006 ◽
Vol 17
(03)
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pp. 331-338
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