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| Global Existence and Blow-Up Results for a Classical Semilinear Parabolic Equation |
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Citation： |
Li MA.Global Existence and Blow-Up Results for a Classical Semilinear Parabolic Equation[J].Chinese Annals of Mathematics B,2013,34(4):587~592 |
| Page view： 1538
Net amount： 1083 |
Authors： |
Li MA; |
Foundation： |
National Natural Science Foundation of China (No. 11271111) and the DoctoralProgram Foundation of the Ministry of Education of China (No. 20090002110019). |
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| Abstract： |
The author studies the boundary value problem of the classical semilinear
parabolic equations
ut ? Δu = |u|p?1u in Ω × (0, T),
and u = 0 on the boundary ?Ω × [0, T) and u = φ at t = 0, where Ω ? Rn is a compact
C1 domain, 1 < p ≤ pS is a fixed constant, and φ ∈ C1
0 (Ω) is a given smooth function.
Introducing a new idea, it is shown that there are two sets W and Z, such that for φ ∈ W,
there is a global positive solution u(t) ∈ W with H1 omega limit 0 and for φ ∈ Z, the
solution blows up at finite time. |
Keywords： |
Positive solution, Global existence, Blow-up, Omega limit |
Classification： |
35J55 |
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