A sufficient condition for blowup solutions of nonlinear heat equations |
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Authors: | Shaohua Chen |
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Affiliation: | Department of Mathematics, University College of Cape Breton, Sydney, NS, Canada B1P 6L2 |
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Abstract: | The author discusses the initial-boundary value problem (ui)t=Δui+fi(u1,…,um) with and ui(x,0)=φi(x), i=1,…,m, in a bounded domain Ω⊂Rn. Under suitable assumptions on fi, he proves that, if φi?(1+ε0)ψi in , for some small ε0>0, then the solutions blow up in a finite time, where ψi is a positive solution of Δψi+fi(ψ1,…,ψm)?0, with ψi|∂Di=0 for i=1,…,m. If m=1, the initial value can be negative in a subset of Ω. |
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Keywords: | Parabolic equation Dirichlet problem Blowup solutions |
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