Unique continuation for hyperbolic equations with memory

A. L. Bukhgeim; G. V. Dyatlov; G. Uhlmann

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Unique continuation for hyperbolic equations with memory

机译：带记忆的双曲方程的唯一延续

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摘要

We prove the unique continuation property for the hyperbolic integro-differential equation utt-△u+,▽u+(x,t)u+∫ t 0 k(x,t-s)u(x,s)ds=0.

机译：我们证明了双曲积分微分方程utt-△u + ，▽u +（x，t）u +∫t 0 k（x，ts）u（x，s）ds的唯一连续性= 0。

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来源
《Journal of inverse and ill-posed problems》 |2007年第6期|共12页
作者
A. L. Bukhgeim; G. V. Dyatlov; G. Uhlmann;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Unique continuation; Carleman weight estimate; integro-differential equation;

机译：唯一连续;卡尔曼权重估计;积分微分方程;

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1. Unique continuation for hyperbolic equations with memory [J] . A. L. Bukhgeim, G. V. Dyatlov, G. Uhlmann Journal of inverse and ill-posed problems . 2007,第6期

机译：带记忆的双曲方程的唯一延续
2. Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients [J] . Cheng J, Lin CL, Nakamura G Proceedings of the American Mathematical Society . 2005,第8期

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3. HARDY'S UNCERTAINTY PRINCIPLE AND UNIQUE CONTINUATION PROPERTY FOR STOCHASTIC HEAT EQUATIONS [J] . Fernandez-Bertolin Aingeru, Zhong Jie ESAIM . 2020,第1期

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4. Carleman Estimates and Unique Continuation Property for Abstract Elliptic Equations [C] . Veli B. Shakhmurov International Conference of Numerical Analysis and Applied Mathematics . 2011

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6. Quantitative unique continuation for the heat equations with inverse square potential [O] . Guojie Zheng, Keqiang Li, Yuanyuan Zhang -1

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7. Strong unique continuation for second-order hyperbolic equations with time-independent coefficients [O] . Sergio Vessella 2020

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8. Uniqueness Theorem for Abstract Hyperbolic Equations with Application to the Uniqueness of the Harmonic Coordinate System in General Relativity [R] . Ramm, A. G., Mishnaevsky, P. A. 1980

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Unique continuation for hyperbolic equations with memory

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