Global existence and blowup solutions for quasilinear parabolic equations |
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| Authors: | Shaohua Chen Deming Yu |
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| Institution: | a Department of Mathematics, Cape Breton University, Sydney, Nova Scotia, Canada
b Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou, China |
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| Abstract: | The authors discuss the quasilinear parabolic equation ut=∇⋅(g(u)∇u)+h(u,∇u)+f(u) with u|∂Ω=0, u(x,0)=?(x). If f, g and h are polynomials with proper degrees and proper coefficients, they show that the blowup property only depends on the first eigenvalue of −Δ in Ω with Dirichlet boundary condition. For a special case, they obtain a sharp result. |
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| Keywords: | Porous medium equation Quasilinear parabolic equation Global existence Blowup solutions |
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