Nontrivial compact blow-up sets of smaller dimension
We provide examples of solutions to parabolic problems with non- trivial blow-up sets of dimension strictly smaller than the space dimension. To this end we just consider different diffusion operators in different variables, for example, ut = (um)xx + uyy + u m or ut = (|ux|p-2u x)x + uyy + up-1.For...
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2008
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v136_n2_p593_PerezLlanos http://hdl.handle.net/20.500.12110/paper_00029939_v136_n2_p593_PerezLlanos |
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| Sumario: | We provide examples of solutions to parabolic problems with non- trivial blow-up sets of dimension strictly smaller than the space dimension. To this end we just consider different diffusion operators in different variables, for example, ut = (um)xx + uyy + u m or ut = (|ux|p-2u x)x + uyy + up-1.For both equations, we prove that there exists a solution that blows up in the segment B(u) = [-L, L] ×{0}⊂ ℝ2. © 2007 American Mathematical Society. |
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