麦克斯韦方程和波动方程的唯一延拓定理
Unique Continuation Theorem for Maxwell's Equations and Wave Equation
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摘要: 研究了麦克斯韦方程和波动方程的唯一延拓性质。用卡勒曼估计方法获得了波动方程的唯一延拓,用积分变换方法导出了麦克斯韦方程唯一延拓,利用所获得的唯一延拓性导出了半线性波动方程的能控性。所得结果具有较重要的理论意义。Abstract: This paper studies the unique continuation properties of the Maxwell's equation and the wave equation. Under some assumed conditions, by using the Carleman estimating method and the integral transformation we obtain the unique continuation properties of the Maxwell's equation and the wave equation. We solve the controllability problem of the semilinear wave equation by these results obtained in this paper.