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| 摘要: |
| 主要研究了Cauchy问题：ut=Δu+up（x）+uq+ku,(x,t)∈RN×(0,1),u(x,0)=u0(x),x∈RN的非负解的爆破性质，其中，01且初值u0(x)充分大时，解u（x，t）在有限时刻爆破；当max{p+,q}≤1时，解u（x，t）对任意初值u0（x）整体存在；在第4部分，讨论了方程的Fujita指标，并给出了解对任意初值爆破的几种情形。 |
| 关键词: Fujita指标 变指标 非线性抛物方程 整体存在 爆破 |
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| Blow-up Properties of Solutions to a Nonlinear Parabolic Equations with Variable Index Reaction Term |
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TANG Shu-qiao,GUO Yan,SONG Shi-qin
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| Abstract: |
| In this paper,we study the blowp-up properties for nonnegative solutions to the following Cauchy problem: ut=Δu+up（x）+uq+ku,(x,t)∈RN×(0,1),u(x,0)=u0(x),x∈RN, here 01 and when initial value u0(x) is sufficiently big.When max max{p+,q}≤1, the solution u(x,t) shows blow-up properties in finite time to any initial value.In section 4,we discuss Fujita indicators of this equation and give several conditions for the solutions blow-up with any initial value. |
| Key words: Fujita index variable index nonlinear parabolic equation global existence blow-up |
