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Unique continuation through hyperplane for higher order parabolic and Schrödinger equations
Communications in Partial Differential Equations ( IF 2.1 ) Pub Date : 2021-02-10 , DOI: 10.1080/03605302.2021.1881110
Tianxiao Huang 1
Affiliation  

Abstract

Consider the higher order parabolic operator t+(Δx)m and the higher order Schrödinger operator i1t+(Δx)m in X={(t,x)R1+n; |t|<A,|xn|<B}, where m and n are any positive integers. Under certain lower order and regularity assumptions, we prove that if solutions to the linear problems vanish when xn>0, then the solutions vanish in X. Such results are global if n > 1, and we also prove some relevant local results.



中文翻译:

高阶抛物线方程和薛定谔方程通过超平面的唯一延续

摘要

考虑高阶抛物线算子 +(-ΔX) 和高阶薛定谔算子 一世-1+(-ΔX)X={(,X)电阻1+n; ||<一种,|Xn|<},其中mn是任何正整数。在某些低阶和正则性假设下,我们证明如果线性问题的解在Xn>0,那么解在X 中消失。如果n  > 1,这样的结果是全局的,我们也证明了一些相关的局部结果。

更新日期:2021-02-10
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