Boundedness and blowup for nonlinear degenerate parabolic equations |
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Authors: | Shaohua Chen |
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Affiliation: | Department of Math, Physics and Geology, Cape Breton University, Sydney, Nova Scotia, Canada, B1P 6L2 |
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Abstract: | The author deals with the quasilinear parabolic equation ut=[uα+g(u)]Δu+buα+1+f(u,∇u) with Dirichlet boundary conditions in a bounded domain Ω, where f and g are lower-order terms. He shows that, under suitable conditions on f and g, whether the solution is bounded or blows up in a finite time depends only on the first eigenvalue of −Δ in Ω with Dirichlet boundary condition. For some special cases, the result is sharp. |
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Keywords: | Porous medium equation Quasilinear parabolic equation Global existence Blowup solutions |
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