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论文类型： 期刊论文

发表时间： 2015-01-01

发表刊物： JOURNAL OF DIFFERENTIAL EQUATIONS

收录刊物： SCIE

卷号： 258

期号： 1

页面范围： 224-241

ISSN号： 0022-0396

关键字： Carleman inequality; Backward uniqueness; Cone domain; Parabolic operator

摘要： Consider the system vertical bar partial derivative(t)u + Delta u vertical bar <= M(vertical bar u vertical bar+vertical bar del u vertical bar), vertical bar u(x, t)vertical bar <= Me-M vertical bar x vertical bar 2 in C-theta x [0, T] and u(x, 0) = 0 in C-theta, where C-theta is a cone with opening angle theta. L. Escauriaza constructed an example to show that such system has a nonzero solution when theta < 90 degrees, and it's conjectured that the system has only zero solution when theta > 90 degrees. Lu Li and V. Sverak proved that the conjecture is true when theta > 109.5 degrees. Here we improve their result and prove that the conjecture is true when theta > 99 degrees by exploring a new type of Carleman inequality, which is of independent interest. (C) 2014 Elsevier Inc. All rights reserved.