On directional blow-up for quasilinear parabolic equations with fast diffusion |
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Authors: | Yukihiro Seki |
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Affiliation: | Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan |
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Abstract: | We discuss blow-up at space infinity of solutions to quasilinear parabolic equations of the form ut=Δ?(u)+f(u) with initial data u0∈L∞(RN), where ? and f are nonnegative functions satisfying ?″?0 and . We study nonnegative blow-up solutions whose blow-up times coincide with those of solutions to the O.D.E. v′=f(v) with initial data ‖u0‖L∞(RN). We prove that such a solution blows up only at space infinity and possesses blow-up directions and that they are completely characterized by behavior of initial data. Moreover, necessary and sufficient conditions on initial data for blow-up at minimal blow-up time are also investigated. |
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Keywords: | Blow-up at space infinity Blow-up direction Minimal blow-up time |
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