The Landis-Oleinik conjecture in the exterior domain

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• 作者：Jie Wu^a ; ^{jackwu@amss.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Liqun Zhang^b ; ¹ ; ^{lqzhang@math.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35K10 ; 35A02 ; 35R45
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：22 October 2016
• 年：2016
• 卷：302
• 期：Complete
• 页码：190-230
• 全文大小：479 K

文摘

In 1974, Landis and Oleinik conjectured that if a bounded solution of a parabolic equation decays fast at a time, then the solution must vanish identically before that time, provided the coefficients of the equation satisfy appropriate conditions at infinity. We prove this conjecture under some reasonable assumptions of the coefficients, which improved the earlier results.