在二维中支持一类非线性演化方程解的性质

Revista Integración Pub Date : 2021-05-19 DOI:10.18273/revint.v39n1-2021003

Eddye Bustamante, José Jiménez Urrea

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引用次数: 0

摘要

在这项工作中，我们考虑形式为∂tu + P(D)u + u^{l}∂xu = 0的方程，其中P(D)是一个二维微分算子，l∈n。我们证明如果u是该方程的一个充分光滑解，使得suppu(0)， suppu(T)∧[−B, B] x[−B, B]对于某个B∈[0,T]，则存在R0>0，使得suppu(T)∧[-R_0,R_0] x [-R_0,R_0]对于每个T∈[0,T]。

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Propiedades del soporte de soluciones de una clase de ecuaciones de evolución no lineales en dos dimensiones

In this work we consider equations of the form ∂tu + P(D)u + u^{l}∂xu = 0, where P(D) is a two-dimensional differential operator, and l ∈ N. We prove that if u is a sufficiently smooth solution of the equation, such that suppu(0), suppu(T) ⊂ [−B, B] × [−B, B] for some B > 0, then there exists R0>0 such that suppu(t) ⊂ [-R_0,R_0]×[-R_0,R_0] for every t ∈ [0, T].

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Revista Integración

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